Mining Community-Level Influence in Microblogging Network...

Research ArticleMining Community-Level Influence in Microblogging NetworkA Case Study on Sina Weibo

Yufei Liu1 Dechang Pi12 and Lin Cui1

1College of Computer Science and Technology Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 211106 China2Collaborative Innovation Center of Novel Software Technology and Industrialization Nanjing Jiangsu 211106 China

Correspondence should be addressed to Dechang Pi dcpinuaaeducn

Received 7 June 2017 Accepted 12 November 2017 Published 4 December 2017

Academic Editor Jia Wu

Copyright copy 2017 Yufei Liu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Social influence analysis is important for many social network applications including recommendation and cybersecurity analysisWe observe that the influence of community including multiple users outweighs the individual influence Existing models focuson the individual influence analysis but few studies estimate the community influence that is ubiquitous in online social networkA major challenge lies in that researchers need to take into account many factors such as user influence social trust and userrelationship to model community-level influence In this paper aiming to assess the community-level influence effectively andaccurately we formulate the problem ofmodeling community influence and construct a community-level influence analysis modelIt first eliminates the zombie fans and then calculates the user influence Next it calculates the user final influence by combining theuser influence and thewillingness of diffusing theme information Finally it evaluates the community influence by comprehensivelystudying the user final influence social trust and relationship tightness between intrausers of communities To handle real-worldapplications we propose a community-level influence analysis algorithm called CIAA Empirical studies on a real-world datasetfrom Sina Weibo demonstrate the superiority of the proposed model

1 Introduction

Community-level influence analysis is an emerging problemwhich can be used in many filed for example recommenda-tion system [1 2] public opinion prediction [3] and cyber-security analysis [4] There are many researchers who areinterested in analyzing the social influence in social networks[5] but rarely assessing the influence in community levelWith the rapid spread of online social networks such asTwitter Facebook and Sina Weibo large amounts of datawith the real world are produced which provide support forthe social influence analysis

How to establish an effective model for analyzing com-munity-level influence has become an important research foronline social network Community-level influence is greaterthan individual-level influence but few researchers havestudied community influence The existing studies establishvarious social influence analysis models [6 7] but theyjust study the influence in the individual level and mostlyignore the existence of a common influence pattern from a

community that includes multiple nodes A large numberof achievements have been obtained on individual-levelinfluence but most of the studies are based on static statisticsmethod [8ndash11] link analysis algorithms [12ndash14] or probabilis-tic models [15ndash17]These studies do not consider whether theuser is willing to receive or diffuse information or what therole of social trust between users is or do not remove zombiefans However these factors are very important for analyzingthe social influence Meanwhile the existing works aboutcommunity-level influence focus on the influence strengthbetween communities and ignore the problem of analyzingthe community-level influence For example Belak et al [18]calculated the community-level influence by only averaginginfluence of all users in a community

An important observation is that zombie fans have nocontribution to the social influence and the willingness ofusers to diffuse information has a certain effect on the accu-racy of calculating social influence and social trust plays animportant role in social influence The trust degree of user Ato user B determines the influence of user B on user A The

HindawiComplexityVolume 2017 Article ID 4783159 16 pageshttpsdoiorg10115520174783159

2 Complexity

more the user A trusts user B the more influence the user Bhas on the user A Because user influence is the basis of thecommunity influence a little carelessness on the former willlead to errors on the later

Aiming to assess the community-level influence effec-tively and accurately we construct a community-level influ-ence analysis model that can assess community influenceBased on our model a community-level influence analysisalgorithm (short for CIAA) is proposed which can assessthe community influencemore effectively and accuratelyThemain idea of our model is as follows First we eliminatethe interference of zombie fans on the social influence tomake the results more accurate Then in the process ofcalculating user influence we consider the social trust anduse the random walk method to calculate the user influenceIn evaluating the userrsquos theme information the user meanwillingness is calculated by exploring the content related tothe userrsquos theme information We combine these two factors(the user influence and the user willingness to diffuse themeinformation) to calculate the user final influence Finally thecommunity-level influence is calculated by comprehensivelystudying the user final influence the social trust and rela-tionship tightness between intrausers of communities Exper-iments are conducted on a real-world dataset crawled fromSina Weibo Comparing with the state-of-the-art algorithm(the averaging user influence algorithm [18]) the results showthat our model is more effective and accurate to evaluate thecommunity-level influence

The contributions of this paper can be summarized asfollows (1) We formulate the problem of analyzing thecommunity-level influence and design a community-levelinfluence analysis model (2)CIAA a community-level influ-ence analysis algorithm based on our model is proposedwhich is effective and reliable to evaluate the communityinfluence of microbloggers from SinaWeibo (3)We conductextensive experiments to assess the performance of the pro-posed model Experimental results on the real-world datasetdemonstrate the superiority of the proposed CIAA

The rest of the paper is organized as follows In Section 2we summarize the related works In Section 3 we proposethe community-level influence analysis model and give anexample to illustrate its working principle and the CIAA isproposed In Section 4 we conduct experiments on the real-world dataset crawled from Sina Weibo and then analyze theperformance of the proposed approach Finally we state theconclusion and future work in Section 5

2 Related Works

Since Katz and Lazarsfeld [19] found that social influenceplays an important role in social life and decision-making inthe 1950s researchers in computer field have spare no effortto study the relevant problems It is found that the popularusers play an important role in adopting innovation socialpublic opinion propagation and guidance group behaviorformation and development [5] and so on

There are a great deal of research efforts to measureindividual-level influence [20 21] typically the ldquoopinionleadersrdquo Existing methods can be categorized into three

types the network structure based methods the user behav-ior based methods and the mutual information based meth-odsThenetwork structure basedmethods are degree central-ity [22] closeness centrality [23] betweenness centrality [24]eigenvector centrality [25] Katz centrality [26] PageRank[27] and clustering coefficient [28] We know that nodedegree essentially means the connection between a node andits neighbors The method based on node degree can intu-itively express this meaning and its computational cost issmaller than other methods [29] These methods are widelyused in measuring the usersrsquo influence in the social networkHowever the methods based on node degree only reflect theconnection between the users and their neighbors and cannotmeasure the usersrsquo influence in the entire social network forthe local influence of users For example based on the com-munity scale-sensitive maxdegree Hao et al [30] proposedan influential users discovering approach called CSSM whenplacing advertisements CSSM uses the degree centralityand neighborrsquos degree to evaluate nodersquos (microbloggers)influence However the algorithm does not consider thecontribution of microblogs to user influence Comparingwith the methods based on the degree the method basedon the shortest path (closeness centrality and betweennesscentrality) can measure the individual-level influence inthe entire social network Nevertheless its computationalcomplexity is higher than the degree centrality method Forexample based on text mining and social network analysisBodendorf and Kaiser [31] proposed an approach to detectopinion leaders in directed graph of user communicationrelationship It can predict tendency of network opinionleaders via closeness centrality and betweenness centralityMoreover measuring the individual-level influence by theshortest path is an ideal status and it is difficult to achievein the real-world application scenarios Besides the methodsbased on randomwalk only consider the structure character-istics of the node while ignoring the behavior characteristicsFor example Xiang et al [32] provided an understandingof PageRank and authority from an influence propagationperspective by performing random walks However theydid not consider the personal attributes to understandingof PageRank as well as the relationship between PageRankand social influence analysis Zhu et al [33] proposed anovel information diffusionmodel calledCTMC-ICMwhichintroduces the continuous-time Markov Chain theory intothe Independent Cascade Model Based on the model theyproposed a new ranking metric called SpreadRank Based oncontinuous-time Markov process Li et al [34] proposed adynamic information propagation model called IDM-CTMPto predict the influence dynamics of social network usersIDM-CTMP defined two other dynamic influence metricsand could predict the spreading coverage of a user withina given time period Zhou et al [35] established new upperbounds to significantly reduce the number of Monte-Carlosimulations in greedy-based algorithms especially at theinitial step Based on the bound they proposed a new upperbound based lazy forward algorithm for discovering the top-119896influential nodes in social networks

The aforementioned models focus only on assessingthe social influence of single individuals However a small

Complexity 3

number of works attempt to build models on the communityinfluence analysis Qi et al [36] applied degree centralitycloseness centrality and betweenness centrality to groups andclasses as well as individuals Latora and Marchiori [37] putforward a group information centrality tomeasure the impor-tance of node setsMehmood et al [38] exploited informationdiffusion records to calculate the influence strength betweendifferent communities Although these works preliminarilystudy the community-level influence none of them focuseson how to measure a communityrsquos influence Belak et al[18] assessed the community-level influence according to theaverage of the all usersrsquo influence in the same communityBecause the distribution of the usersrsquo influence is uneven indifferent communities average based method is inequitableto bigger communities while summation based method isinequitable to smaller ones At present community-levelinfluence analysis is still a challenging problem

3 Proposed Methodology

We construct our model and implement the correspondingalgorithm in this section First we give the related definitionsin Section 31 Then we propose the community-level influ-ence analysis model for microbloggers Next we describe theworking principle of ourmodel via an example in Section 32Finally the community-level influence analysis algorithm isproposed in Section 33

31 Related Definitions and Community-Level InfluenceAnalysis Model

311 Related Definitions Social networks and communitiesare described as follows a typical social network can berepresented as a bipartite graph119866 = 119881 119864119881 is a set of nodes(users) in a social network and 119864 is a set of edges used todescribe the relationships between nodes A community canbe represented as a subgraph of a social network that is 119862 =119862119881 119862119864 119862119881 sube 119881 is a set of users in a community 119862119864 sube 119864is a set of relationships between users within a communityA node is defined as a user within the community if heshebelongs to the community otherwise heshe is defined asa user outside the community The set of users outside thecommunity is written as UOC Modeling and calculating thecommunity influence of 119862119894 are the basis of our work and theobjective function of our model is as follows

CI (119862119894) = 119891 (119866 119862119894) (1)

CI(119862119894) denotes the community influence of the commu-nity 119862119894 and the function 119891(119866 119862119894) indicates that the assess-ment method is based on 119866 and 119862119894 There are two entities(ie users and communities) which can produce influenceTo study the community-level influence we give the relateddefinitions as follows

Definition 1

Trust A node in a social network has a certain trust degreein other nodes according to its past contact with other nodesor the reputation of other nodes [39 40] According to the

different sources of trust we divide the trust into direct trustand indirect trust

(1) Direct Trust (DT) Assume that the node V is the entry nodeof the node 119906 indicating that there is contact between 119906 andV According to the previous contacts and the reputation of 119906V will have direct trust on 119906

(2) Indirect Trust (IT) Assume that the node 119906 is the reachablenode of the node V Vwill have indirect trust on 119906 because thereputation of 119906 can be transmitted to V

Users not only have mutual trust but also mutually influ-ence each other According to the different sources of influ-ence this paper divides the influence into direct influence andindirect influence

Definition 2

(1) Direct Influence (119863119868) Assume that the node V is the entrynode of the node 119906 119906 will have an influence on V that is 119906produces direct influence on V

(2) Indirect Influence (II) Assume that the node 119906 is areachable node of the node V 119906 will have an influence onV through transmission layer by layer that is 119906 producesindirect influence on V

In order to assess the overall influence of 119906 on V we definethe user combined influence

Definition 3

User Combined Influence (UCI) Because V has direct trustor indirect trust to 119906 and 119906 has direct influence or indirectinfluence on V we comprehensively combine the four factorsto calculate the combined influence of 119906 on V

Definition 4

(1) User Influence (UI) User influence refers to the influenceof individual on other users

(2) Community Influence (CI) Community influence is theoverall influence of the community which is formed by theUI of all the users in the community and the communityrsquosself-factors

Definition 5

Mean Willingness to Diffuse Theme Information (119872119882) Incommunities some users receiving the theme informationmay not diffuse it some users prefer to post their own blogand some users prefer to forward othersrsquo blog We assessthe community influence by taking into account the diffu-sion of information between users MW represents a userrsquowillingness to diffuse the information of a blog The themeinformation of the user 119906 is stored in the set 119879(119906) =1199051199061 1199051199062 119905119906119895 where 119905119906119895 represents the userrsquos 119895th themeinformation If 119905119906119895 is diffused in a social network a pathmap 119892119906119895 is formed to describe the propagation path Westore the path graphs formed by 119879(119906) in the set 119892(119906) =1198921199061 1198921199062 119892119906119895

4 Complexity

Data sources

The community influenceThe user final influence

Mean willingness to diffuse theme information

User influence User integratedinfluence Community size Relationship

tightness

User information table

User theme information

(microblog) tableUser fans table User attention

table

Data preprocessing

Eliminating zombiefans

Figure 1 The framework of the proposed model

u

vUI(v)

MW(u)

UI(u)

MW(u)

UI(u)

MW()

UI(v)

CS

Step 1 Step 2 Step 3

v

v

v u

uu

u

v

MW()

Stv

＄ＣffＯtv

Sut

＄ＣffＯut

UII(C)

RT(C)

Figure 2 The working steps of the community-level influence analysis model

312 Model Framework Our model consists of four mod-ules data preprocessing module data source module theuser final influence module and the community influencemodule Figure 1 shows our model framework

Data preprocessing module is used to eliminate zombiefans We judge the zombie fans from the behavior dimensionand time dimension Behavior dimension is based on theamount of theme information posted by the user and thefansrsquo influence of the user Time dimension is based on theuser login frequency and the frequency of diffusing themeinformation Finally the data preprocessing results are storedto the data source

Data source module is responsible for providing the rele-vant data needed for influence analysis We establish the userinformation table the microblog table the user fans infor-mation table and the user attention table to access the userrsquosrelevant information efficiently

The user final influence module first calculates the meanwillingness to diffuse theme information for each user in acommunity and then calculates the userrsquos influence Next itcombines these two results to get the user final influence

The community influence module first calculates thecommunity size the tightness of user relationship and theuser-integrated influence in the community and then evalu-ates the community influence by integrating the three factors

32 Working Principle In this subsection we introduce theworking principle of eachmodule in themodel framework in

detail We assume that 119906 and V are two users in community119862 After performing data preprocessing Figure 2 shows theworking principle where the mathematical notations will bedescribed in the following subsections in detail

The working principle can be described as the followingsteps

Step 1 Calculate the DiffuV and 119878V of V Then calculate theMW(V) of V Finally calculate UI(V) of V

Step 2 According to Step 1 calculate the MW(V) and UI(V)of 119906

Step 3 Integrate MW and UI to calculate the UII(119862) Thencalculate CS and RT(119862) Finally combine the three factors tocalculate the community influence

321 Data Preprocessing In microblogging networks someusers of ulterior motives or business purpose lead to produc-ing the zombie fans According to the definition in [41] zom-bie fans are the users who are fake fans generated and main-tained mostly for economic purpose Zombie fans certainlyinterfere in analyzing the social influence A small numberof empirical researches have been conducted on recognizingzombie fans [41ndash43]The existing studies were mostly subjectto the Twitter platform

Presently researchers generally detect the zombiefans based on the amount of attention the number of fans

Complexity 5

(1) Input 119881 119864 LF DAF NUI NAU NUF(2)Output 119866 = (119881 119864)(3) Select the users who are the last 10 of the login frequency and whose login

time interval is greater than 7 days into the set LF(4) Put the users with the top 10 of the diffusing advertisement frequency into

the set DAF(5) Select the users who are the last 10 of the number of userrsquo theme

information into the set NUI(6) Put the users with the top 10 of the attention users into the set NAU(7) Put the users with the number of fans between 10ndash200 into the set NUF(8) ZF = LF cap DAF capNUI cap NAU cap NUF(9) Update 119881 = 119881 minus ZF and 119864 = 119864 minus 119864ZF(10) return 119881 119864

Algorithm 1 Eliminating zombie fans

original and forward information frequencies and otherbasic attributes With the ever-changing escalation of zombiefans zombie fans will produce more features [44] Theexisting feature-based methods to eliminate zombies maygradually fail We observe that because zombie fans areoccasionally managed via software program or a few peoplebehind zombie fans often rarely speak even seldom log in orno longer are used and their behaviors can be vastly differentwith ordinary users in profile information and contentsMoreover no matter how the features of zombie fanschange they can be split into time dimension and behaviordimension Thus it is reasonable to recognize zombie fansfrom the time dimension and behavior dimension and it ismore able to adapt to the needs of detecting zombie fans inmicroblogging networks

According to expert knowledge criteria [45] in thetime dimension we assess zombie fans from the user loginfrequency and the diffusing advertisement frequency Thustime dimension includes login frequency (LF) and diffusingadvertisement frequency (DAF) Login frequency refers tothe number of logins in a period The lower the frequencyof login is the higher the probability of the user becomingzombie fans is The login frequency is calculated as follows

LF = Δ119905LoginNumberΔ119905 (2)

where LoginNumber indicates the number of logins Thehigher the diffusing advertisement frequency is the higherthe probability of the user becoming zombie fans is Thediffusing advertisement frequency is calculated as follows

DAF = Δ119905NumberOfDiffusingAdvertisementΔ119905 (3)

where NumberOfDiffusingAdertisement indicates the num-ber of diffusing advertisement frequencies

For the same reason in the behavior dimension we assesszombie fans from the amount of user theme information andthe individual influence of the userrsquos fans Thus we take intoaccount the number of user theme information (NUI) thenumber of attention users (NAU) and the number of userrsquosfans (NUF)

To ensure that the criteria of the parameters are reliablethe corresponding criteria are obtained by prior knowledgeexpert knowledge or experimental trial For example weselect the users who are the last 10 of the login frequencyand whose login time interval is greater than 7 days into theset LF To reduce the amount of calculation we filter all usersin a microblogging network If a user has a certified user inhisher fans the user is not considered a zombie fan If a userdoes not have a certified user in hisher fans the details toeliminate zombie fans can be described in Algorithm 1

As we can see that unlike the classification and patternrecognition the proposedmethod to eliminating zombie fansdoes not require labeled data and trainingmodel It is effectiveand easy to use in practice

322 The User Final Influence The traditional models aresimple not taking into account the degree of social trustbetween users and the userrsquos willingness to diffuse themeinformation However the two factors are important to theuser final influence In this paper the user final influence iscalculated by integrating the MW and UI Because the influ-ence of a user on other users is related to the userrsquos willingnessto exert hisher influence the bigger the value of MW thegreater the probability of the user diffusing a theme infor-mation UFI is calculated as follows

UFI (119906) = MW (119906) times UI (119906) (4)

Mean Willingness to Diffuse Theme Information The higherfrequency of diffusing theme information means a higheruser influence because more users will know the userTherefore MW reflects the probability that a user has high-impact in a microblogging network The parameter 119878V119879119906119895indicates the state of receiving theme information for the userV as follows119878V119905119906119895

=

0 The user has never received the theme information

1 The user has received the theme information

(5)

The initial value of 119878V119879119906119895 is set to 0 Meanwhile to knowthe result of V diffusing the theme information 119905119906119895 we observe

6 Complexity

u1 u2

u4u5

u3

1

2

3

(a)

u1 u2

u4u5

u3

1

2

3

(b)

u1 u2

u4u5

u3

1

2

3

(c)

u1 u2

u4u5

u3

1

2

3

(d)Figure 3 An example of calculating MW there are five users inside a community that is 1199061 1199062 1199063 1199064 and 1199065 There are three users outsidethe community that is V1 V2 and V3 (a) shows the relationship between these users (b) shows the diffusion of theme information from 1199061(c) also shows the diffusion of theme information from 1199061 (d) shows the diffusion of theme information from 1199062

119892119906119895 The parameter DiffuV119905119906119895 indicates whether V diffuses thetheme information that heshe received

DiffuV119905119906119895 =

0 outdegree le 01 others

(6)

When the outdegree of V is greater than 0 it indicatesthat V has already diffused the theme information otherwiseV has never diffused the theme information The number ofusers receiving theme information is written as NRTI andthe number of users diffusing theme information is writtenas NDTI

NRTI = sum119906isin(119881minusV)

sum119905119906119895isin119879(119906)

119878V119905119906119895

NDTIV = sum119906isin(119881minusV)

sum119905119906119895isin119879(119906)

DiffuV119905119906119895 (7)

MW is calculated as

MW (V)

= 120579 times (NDTIVNRTIV) + (1 minus 120579) times sum119906isinIn(V)MW (119906) times 119908 (119906)num119878

+ |NP (V)|num119878

(8)

where 119908(119906) = 1outdegree(119906) MW(V) is the MW of V120579 isin [0 1] is the weight NP(V) represents the total numberof theme information posts by V In(V) is the set of indegreenodes of V 119908(119906) represents the weight of the user 119906 which isdetermined by hisher outdegree num119878 is the total number of119892119906119895 The initial value of MW(V) is set as 1 We give an examplefor calculating MW in Figure 3

Assume that the MW of all users initially are 1 120579 = 06and then calculate the MW as follows

(1)119872119882(1199061) From Figures 3(b)ndash3(d) we have num119904 = 3 For1199061 heshe posts two-theme information which forms twotheme information graphs in Figures 3(b) and 3(c) Thus weget the set 119879(1199061) (|119879(1199061)| = 2) From Figure 3(d) NRTI1199061 =1 NDTI = 0 because the outdegree of node 1199061 is 0 and1199061 forms its one theme information graph The MW(1199061) iscalculated as follows

119860 (1199061) = 1199062 1199065 119861 (1199061) =

119908 (1199062) =12

119908 (1199065) =14

MW (1199061)

= 06 times (01) + 04 times (1 times (12) + 1 times (14))3 + 23= 2330

(9)

(2)119872119882(1199062) Similar to the calculation of MW(1199062) we havethe set119879(1199062) |119879(1199062)| = 1 FromFigures 3(b) and 3(c) we haveNDTI1199062 = 1 NRTI1199062 = 2 MW(1199062) is calculated as follows

119860 (1199062) = 1199061 1199064 119861 (1199062) = 119908 (1199062) = 1

119908 (1199064) =13

MW (1199062) =06 times (12) + 04 times (1 times 1 + 1 times (13))

3+ 13 =

118

(10)

Complexity 7

Similarly for 1199063 1199064 and 1199065 we have

NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13

MW (1199064) =06 times (33) + 04 times (1 times 1 + 1 times (13) + 1 times (12) + 1 times 1 + 1 times (13))

3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1

MW (1199065) =06 times (23) + 04 times (1 times (13) + 1 times (13) + 1 times (13) + 1 times (13) + 1 times 1)

3 + 0 = 49 (11)

The User Influence There are mutual impact and mutualtrust between users Social trust plays an important role incalculating the user influence Shehe is impacted by othersincluding users inside and outside the community

(1) Calculating Direct Trust and Direct Influence If V is anentry node of 119906 then V will have direct trust on 119906

DTV119906 =RU (119906)

outdegree (V)

RU (119906) =sum119908isinIn(119906) RU (119908)indegree (119906)

(12)

where DTV119906 is the direct trust of V on 119906 RU(119906) is thereputation of user 119906 In(119906) is the set of entry nodes of 119906 andRU(119906 larr 119908) is the reputation of the entry neighbor 119908 of 119906The value of RU(119906) depends on the average reputation of all119906rsquos entry neighbors For each node we give the initial directtrust value 01 In Figure 3(a) we calculate the direct trust on1199061 from other nodes as follows

RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)

119906 has a direct influence on V as follows

DI119906V =119868 (119906 larr V)

outdegree (V)

119882 (119906 larr997888 V) = |theme (V 119906)|NRTIV

(14)

where DI119906V is the direct influence of 119906 on V 119868(119906 larr V) isthe degree of interest of V to 119906 |theme(V 119906)| is the amountof the theme information from 119906 in the receiving themeinformation of V

In Figure 3 we calculate the direct influence on 1199061produced by other users as follows

119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)

In Figure 3(a) we have

DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1

DI1199061V3 =00 (written as 0)

(16)

(2) Indirect Trust and Indirect Influence If 119906 is the reachablenode of V then V will have indirect trust on 119906 as follows

ITV119906 =RU (119906)minV119906

(17)

Complexity 9

ITV119906 is Vrsquos indirect trust on 119906 minV119906 is the length of theshortest path from V to 119906

In Figure 3(a) we calculate the indirect trust on 1199061 gainedfrom other nodes as follows

IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)

119906 has an indirect influence on V as follows

II119906V =119868 (119906 larr V)minV119906


(19)

In Figure 3(a) we calculate the indirect influence of othernodes on 1199061 as followsThe calculation of 119868 is the same as theabove formula

II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05

II1199061V3 =00 (written as 0)

(20)

(3) User Combined Influence Assuming that V can reach 119906through a path we introduce the factor 120582 (120582 isin [0 1])

If V is the entry node of 119906 the combined influence of 119906 onV is

UCI119906V = 120582DI119906V + (1 minus 120582)DTV119906 (21)

If V is not an entry node of node 119906 but 119906 is a reachable nodeof V the combined influence is

UCI119906V = 120582II119906V + (1 minus 120582) ITV119906 (22)

Assume 120582 = 03 In Figure 3 we calculate the combined influ-ence of other nodes on 1199061 as follows

1199062 is the entry node of 1199061 then we have UCI11990611199062 =03 times 05 + 07 times 004 = 01781199064 is the entry node 1199061 then we have UCI11990611199064 = 03 times0334 + 07 times 004 = 012821199065 is the entry node of 1199061 then we have UCI11990611199065 =03 times 0133 + 07 times 002 = 00539V1 is the entry node of 1199061 then we have UCI1199061V1 =03 times 0334 + 07 times 004 = 01282V2 is the reachable node of 1199061 then we have UCI1199061V2 =03 times 05 + 07 times 004 = 0178

(4) User Influence User influence is got by combining allusersrsquo influence

UI (119906) =sumVisinSUCP(119906)UCI119906V|SUCP (119906)| (23)

where SUCP represents a set of users that can reach 119906 througha certain path For example in Figure 3 the user influence of1199061 is calculated as follows

UI (1199061)

=UCI11990611199062 + UCI11990611199064 + UCI11990611199065 + UCI1199061V1 + UCI1199061V2

5= 0133

(24)

Whenwe getMW(1199061) andUI(1199061) the user final influencecan be calculated according to (4)

323 Community Influence The community influence iscomposed of the usersrsquo interaction inside and outside thecommunity In this paper we consider it from three factorsthat is the user-integrated influence the community size andthe degree of relationship tightness among users inside thecommunity

User-integrated influence (UII) is integrated from thefinal influence of all users within the community

UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)

where UII(119862119894) is UII of the community119862119894119862119881(119906) is the set ofusers inside community 119862119894

The community size (CS) is important to the calculationof the community-level influence The larger the number ofusers in a community is the greater the influence of thecommunity becomes The formula is as follows

CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)

where |119862119881(119862119894)| represents the number of users in a commu-nity and max(119881) represents the total number of users in thesocial network

10 Complexity

Input 119866 = 119881 119864 119862 119879(119906) 119892(119906) UII = 0 120591 120588 RT = 0Output community influence(1) for 119894 = 0 to |119881| do(2) MW(119894)(3) UI(119894)(4) end for(5) for 119895 = 0 to |119862119881| do(6) UII(119895) = MW(119895) times UI(119895) + UII(119895)(7) end for(8) CS(119862)(9) for 119894 = 0 to |119862119881| do(10) RT(119862119894) =

sum119906isin119862119881(119862119894)(outdegree(119906) + indegree(119906))119862119881(119862119894)

(11) end for(12) CI(119862119894) = 120591 times UII(119862119894) + 120588 times CS + (1 minus 120591 minus 120588) times RT(119862119894)(13) return CI(119862119894)

Algorithm 2 Community-level influence analysis algorithm (CIAA)

The degree of relationship tightness (RT) represents thedegree of closeness between users inside a community Wedescribe it from the userrsquos outdegree and indegree as follows

RT (119862119894) =sum119906isin119862119881(119862119894) (outdegree (119906) + indegree (119906))

119862119881 (119862119894) (27)

Therefore we calculate the CI as follows

CI (119862119894) = 120591 times UII (119862119894) + 120588 times CS + (1 minus 120591 minus 120588)

times RT (119862119894) (28)

where 120591 and 120588 (120591 120588 isin [0 1]) are used to distinguish theimportance of different factors

33The Proposed Algorithm According to the above descrip-tion we propose a community-level influence analysis algo-rithm called CIAA in a pseudo-code format in Algorithm 2It can be seen from the algorithm that the total timecomplexity is 119874(119899) This means that our algorithm can beapplied on large-scale social dataset

4 Experiments

We conduct experiments to validate the effectiveness of theproposed approach on a real-world microblogging networkIn this section we describe the experimental setup followedby the discussion of experiment results

41 Dataset The real-world dataset in this paper is crawledfrom Sina Weibo by Weibo crawler Similar to a hybrid ofTwitter and Facebook SinaWeibo is one of the most popularsites in China It has more than 33 of the Internet usersin China and its market penetration is equivalent to that ofTwitter in the United States As released by the Sina Weiboas of June 2016 the active users from different social andcultural backgrounds have reached 282 million monthly and868 million daily Moreover there are nearly 100million new

Table 1 Data structure and description of the user information

Features DescriptionUserID Userrsquo IDIsVIP Authenticated userFansNum Number of fansAttenNum Number of attention usersThemeAmo Amount of theme informationTag Userrsquo labelTime Login time

Table 2 Data structure and description of the user theme informa-tion (microblogs)

Features DescriptionThemeID Theme information IDThemeFromID Source ID of theme informationProNum Number of processesThemeClass Theme information classPTime Post time of theme information

Table 3 Data structure and description of the user fans

Features DescriptionUserID Userrsquo IDFansID Fansrsquo ID

microblogs every day They promote and disseminate viewsand attitudes on business culture education and so forthThe crawled data includes 20151129 microblogs 932578467comments and 9218 users In this paper we collected morethan 1000 users from the crawled dataset and divided therelated information into Tables 1 2 3 and 4 for data sourcesaccording to our model framework They are stored in txt-formatted files

Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)

Figure 4 (a) is the outdegree distribution and (b) is the degree distribution

Table 4 Data structure and description of the user attention

Features DescriptionUserID Userrsquo IDAttenID User-attended ID

Table 5 Parameters for experiments

Symbol Description Value119881 The total number of nodes 1127119862119881 The total number of nodes in the community 20120582 Parameter 03120579 Parameter 05120591 Parameter 05120588 Parameter 03

42 Experimental Setting All experiments are conducted ona PC with Intel Core i5 processor 8GB RAM According toprior knowledge we set the parameters of the experiments asTable 5

43 Results

431 Community Structure Analysis In order to mine andstudy the characteristic of community we plot the outdegreedistribution and degree distribution of users in communityIn a directed social network the indegree of nodes is thenumber of fans of the user The outdegree of nodes is theamount of the userrsquos attention Figure 4 shows the outdegreeand degree distribution of data sources

As shown in Figure 4 the outdegree distribution and thedegree distribution of Sina Weibo dataset follow the power-law distribution which indicates that the social networkcomposed of the dataset is a scale-free network

432 Eliminating Zombie Fans In order to improve theaccuracy of our model we remove zombie fans Accordingto the eliminating zombie fans method in Algorithm 1 wefinally remove 12 zombie fans as shown in Table 6

As shown in Table 6 the three sets are NUI NAU andNUF The little black boxes in Table 6 represent the sharedusers of three sets and they are the same as the shared usersfrom time dimension and behavior dimension Thereforethe shared users will be removed We compare the userfinal influence without the zombie fans with the user finalinfluence with the zombie fans as shown in Table 7

From Table 7 the result of the comparison shows thatthe accuracy of the UFI with zombie fans for the actual userranking is only 60 It is concluded that the elimination ofzombie fans is very important for the accuracy of the userfinal influence

433 Accuracy Analysis of the User Final Influence We cal-culate the user final influence of users in community but wecompare the top ten users for simplicity The top 10 user finalinfluences and their related information are shown in Table 8

According to the UFI ranking in Table 8 we find thatthese users are authenticated user It is concluded that theauthenticated users are more influential in microbloggingnetworks There are two reasons for this phenomenon Firstthe majority of well-known users are authenticated usersand the influence of well-known users is larger than the user

12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast

lowastlowastlowast843

320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13

Table 7 Comparison of the user final influence

User ID UFI withoutzombie fans

UFI withzombie fans

The actualrankings

263 lowast lowast lowast lowast023 1 3 1511 lowast lowast lowast lowast843 2 2 2519 lowast lowast lowast lowast020 3 1 3508 lowast lowast lowast lowast496 4 4 4550 lowast lowast lowast lowast598 5 5 5267 lowast lowast lowast lowast724 6 6 6365 lowast lowast lowast lowast215 8 8 7299 lowast lowast lowast lowast593 7 7 8522 lowast lowast lowast lowast989 9 9 9194 lowast lowast lowast lowast451 10 10 10

Table 8 Top 10 user information of the UFI

UFIranking User ID Number of

fansNumber of

blogsAuthenticated

or not1 263lowastlowastlowastlowast023 128 1515 12 511lowastlowastlowastlowast843 282 1282 13 519lowastlowastlowastlowast020 66 101 14 508lowastlowastlowastlowast496 261 5471 15 550lowastlowastlowastlowast598 14 22 16 267lowastlowastlowastlowast724 823 1452 17 299lowastlowastlowastlowast593 158 109 18 365lowastlowastlowastlowast215 177 945 19 522lowastlowastlowastlowast989 13 29 110 194lowastlowastlowastlowast451 69 11 1

average influence Second the authenticated userrsquos identity istransparent which makes the user have higher social trustTable 8 also shows that the user final influence needs to beconsidered from the quality of the user fans the number ofuser microblogs and user authentication

Table 9 and Figure 5 show the comparison between theUFI method and the microblog-fans ranking algorithmTable 9 shows the UFI method ranking and the correspond-ing ranking via microblog-fans ranking algorithm Figure 5shows the overall ranking order via the microblog-fansranking algorithm

It can be seen from Table 9 and Figure 5 that the UFIranking is almost completely different from the microblog-fans ranking Overall according to the UFI method thenumber of microblogs and fans of the top users must reach acertain quantity to support individual influence Thus thenumber of microblogs and fans is a factor of measuring influ-ence in UFI method However social trust between users canhelp improve individual influence in the UFI method

The user final influence is an experimental evaluation ofthe user and there is no existing dataset with its comparisonWe can only refer to the ranking of the user influence fromsome affiliations Based on the ranking of user influenceprovided by Sina Weibo official we verify the calculation

Table 9 Comparison of UFI method with microblog-fans rankingalgorithm


fansNumber of

blogs

Microblog-fans

ranking1 263lowastlowastlowastlowast023 128 1515 32 511lowastlowastlowastlowast843 282 1282 43 519lowastlowastlowastlowast020 66 101 84 508lowastlowastlowastlowast496 261 5471 15 550lowastlowastlowastlowast598 14 22 66 267lowastlowastlowastlowast724 823 1452 27 299lowastlowastlowastlowast593 158 109 78 365lowastlowastlowastlowast215 177 945 59 522lowastlowastlowastlowast989 13 29 1010 194lowastlowastlowastlowast451 69 11 9

Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r

Figure 5 The overall ranking via the microblog-fans ranking algo-rithm

method proposed in this paper We compare the resultsof the proposed method with the official ranking to verifythe correctness of the user final influence Because eachmicroblogging platform has its own influence calculationmethod we cannot numerically compare the results but wecompare the results from the relative position that is rank-ing If the influence rankings of the two methods are in thesimilar order we consider the results of the influence analysisto be similar The comparison of the users ranking by SinaWeibo officially and UFI method is shown in Table 10

In Table 10 the user final influence calculation methodand the user actual ranking are mainly the same but havingthe user pair of 299 lowast lowast lowast lowast593 and 365 lowast lowast lowast lowast215 Thatis because user influence ranking by Sina Weibo emphasizesthe number of microblogs and fans and the number ofmicroblogs and fans of user 299lowastlowastlowastlowast593 and user 365lowastlowastlowastlowast215 is largely different However the UFI method considersthe factors of influence more reasonably

14 Complexity

Table 10 Comparison of user actual ranking with UFI ranking

User ID The actualranking UFI value UFI ranking


UFIMicroblog-fans

Parameter pairs (lamda theta)

00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)

Figure 6 Comparison of accuracy of two methods with different 120582and 120579

Considering the results of Sina Weibo official as the stan-dard the accuracy of UFI method will change with different120582 and 120579 as shown in Figure 6

From Figure 6 it can be seen that the UFI methodaccuracy changes with the different 120582 and 120579 When 120582 = 03120579 = 05 UFI method has the highest accuracy Therefore theparameter pair (03 05) is used for other experiments Wealso find that the UFI method is more accurate than themicroblog-fans ranking algorithm Moreover this experi-ment indicates the importance of the user willingness todiffusing theme information in the accuracy of the userinfluence

434 Accuracy Analysis of CIAA Because the existing stud-ies of community influence are few we compare the proposedalgorithm CIAA with the averaging user influence algorithm(AI) We set different parameters pair 120591 and 120588 for comparingthe two algorithmsThen we can calculate the correspondingcommunity influence as shown in Figure 7

Figure 7 shows that the results of the CIAA are changingwith the different parameter values When 120591 = 05 and 120588 =02 the results of the two algorithms are closest That is

CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)

Figure 7 The community-level influence by two measuring algo-rithms with different (120591 120588) pairs

because the AI algorithm is mainly the weighted average ofthe user influence and the CIAA is the integration of theuser-integrated influence the community size and the degreeof relationship tightness among users inside the communityThe greater the proportion of the user final influence thecloser the results of the two algorithms Therefore the pro-posed algorithm outperforms the state-of-the-art baselinealgorithm

5 Conclusion

In this paper we studied the emerging problem on how tomodel community-level influence Online social networksespecially microblogging networks are more and moreimportant in our daily life Previous works can effectivelycopewith the individual influence inmicroblogging networkbut they rarely evaluate the social influence in communitylevel which outweighs the individual influence We definedthe related concepts for the community-level influence andconstructed a model that combined the user influence socialtrust and relationship tightness of intrausers in a communityto reveal the community-level influence appropriately Weproposed the algorithm CIAA to cope with the real-worldapplications We conducted empirical studies on a real-world microblogging crawled from Sina Weibo where theCIAA outperformed the state-of-the-art baseline algorithmTo the best of our knowledge the proposed approach hasa significant effect on community influence in microblog-ging network The highlights of this paper can be summa-rized as follows (1) formulating the problem of analyzingcommunity-level influence and designing a community-level influence analysis model (2) proposing community-level influence analysis algorithm called CIAA to cope withreal-world microblogging applications and (3) extensivelydemonstrating the superiority of the proposed method Inthe future work we plan to extend the proposed method toassess the community influence in dynamic online social net-work

Complexity 15

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China under Grants U1433116 and61702355 in part by the Fundamental Research Funds forthe Central Universities under Grant NP2017208 and in partby the Funding of Jiangsu Innovation Program for GraduateEducation under Grants KYLX15 0324 and KYLX15 0321

References

[1] L Yao Q Z Sheng A H H Ngu J Yu and A Segev ldquoUnifiedcollaborative and content-based web service recommendationrdquoIEEE Transactions on Services Computing vol 8 no 3 pp 453ndash466 2015

[2] J Wu S Pan X Zhu C Zhang and X Wu ldquoMulti-instanceLearning withDiscriminative BagMappingrdquo IEEE Transactionson Knowledge and Data Engineering pp 1ndash16 2018

[3] D Ghadiyaram and A C Bovik ldquoMassive online crowdsourcedstudy of subjective and objective picture qualityrdquo IEEE Transac-tions on Image Processing vol 25 no 1 pp 372ndash387 2016

[4] T Cruz L Rosa J Proenca et al ldquoA Cybersecurity DetectionFramework for Supervisory Control and Data AcquisitionSystemsrdquo IEEE Transactions on Industrial Informatics vol 12no 6 pp 2236ndash2246 2016

[5] D Kim D Hyeon J OhW-S Han andH Yu ldquoInfluencemax-imization based on reachability sketches in dynamic graphsrdquoInformation Sciences vol 394-395 pp 217ndash231 2017

[6] G Wang W Jiang J Wu and Z Xiong ldquoFine-grained feature-based social influence evaluation in online social networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 25no 9 pp 2286ndash2296 2014

[7] J M Hofman A Sharma and D J Watts ldquoPrediction and ex-planation in social systemsrdquo Science vol 355 no 6324 pp 486ndash488 2017

[8] S Myers and J Leskovec ldquoThe bursty dynamics of the twitterinformation networkrdquo in Proceedings of the 23rd InternationalConference on World Wide Web WWW 2014 pp 913ndash923Republic of Korea April 2014

[9] Y Liu Q Li X Tang N Ma and R Tian ldquoSuperedge predic-tion What opinions will be mined based on an opinion super-network modelrdquoDecision Support Systems vol 64 pp 118ndash1292014

[10] R DeCaux C Smith D Kniveton R Black andA PhilippidesldquoDynamic small-world social network generation throughlocal agent interactionsrdquo Complexity vol 19 no 6 pp 44ndash532014

[11] JWu S Pan X Zhu C Zhang andP S Yu ldquoMultiple structure-view learning for graph classificationrdquo IEEE Transactions onNeural Networks and Learning Systems pp 1ndash16 2017

[12] L Zhu D Guo J Yin G V Steeg and A Galstyan ldquoScalabletemporal latent space inference for link prediction in dynamicsocial networksrdquo IEEE Transactions on Knowledge and DataEngineering vol 28 no 10 pp 2765ndash2777 2016

[13] S-Y Tan J Wu L Lu M-J Li and X Lu ldquoEfficient networkdisintegration under incomplete information The comic effect

of link predictionrdquo Scientific Reports vol 6 Article ID 229162016

[14] J Wu S Pan X Zhu C Zhang and X Wu ldquoPositive and unla-beled multi-graph learningrdquo IEEE Transactions on Cyberneticsvol 47 no 4 pp 818ndash829 2017

[15] A Almaatouq L Radaelli A Pentland and E Shmueli ldquoAreyou your friendsrsquo friend Poor perception of friendship tieslimits the ability to promote behavioral changerdquo PLoS ONE vol11 no 3 Article ID e0151588 2016

[16] Q Fang J Sang C Xu and Y Rui ldquoTopic-sensitive influencermining in interest-based social media networks via hypergraphlearningrdquo IEEE Transactions on Multimedia vol 16 no 3 pp796ndash812 2014

[17] J Wu S Pan X Zhu and Z Cai ldquoBoosting for multi-graphclassificationrdquo IEEE Transactions on Cybernetics vol 45 no 3pp 416ndash429 2015

[18] V Belak S Lam and C Hayes ldquoTowards maximising cross-community information diffusionrdquo in Proceedings of the 2012IEEEACM International Conference on Advances in SocialNetworks Analysis and Mining ASONAM 2012 pp 171ndash178Turkey August 2012

[19] P F Lazarsfeld Personal Influence The Part Played by People inthe Flow ofMass Communications Transaction Publishers NewYork NY USA 2006

[20] C Dong Y Zhao and Q Zhang ldquoAssessing the influence ofan individual event in complex fault spreading network basedon dynamic uncertain causality graphrdquo IEEE Transactions onNeural Networks and Learning Systems vol 27 no 8 pp 1615ndash1630 2016

[21] NMa andY Liu ldquoSuperedgeRank algorithm and its applicationin identifying opinion leader of online public opinion supernet-workrdquo Expert Systems with Applications vol 41 no 4 pp 1357ndash1368 2014

[22] X Tang JWang J Zhong andY Pan ldquoPredicting essential pro-teins based on weighted degree centralityrdquo IEEE Transactionson Computational Biology and Bioinformatics vol 11 no 2 pp407ndash418 2014

[23] M K Tarkowski P Szczepa T Rahwan T P Michalak andM Wooldridge ldquoCloseness centrality for networks with over-lapping community structurerdquo in Proceedings of the in Thir-tieth AAAI Conference on Artificial Intelligence pp 622ndash629Phoenix Ariz USA 2016

[24] N Kourtellis G De Francisci Morales and F Bonchi ldquoScalableOnline Betweenness Centrality in Evolving Graphsrdquo IEEETransactions on Knowledge and Data Engineering vol 27 no 9pp 2494ndash2506 2015

[25] G Lohmann D SMargulies A Horstmann et al ldquoEigenvectorcentrality mapping for analyzing connectivity patterns in fMRIdata of the human brainrdquo PLoS ONE vol 5 no 4 Article IDe10232 2010

[26] P Grindrod and D J Higham ldquoA matrix iteration for dynamicnetwork summariesrdquo SIAM Review vol 55 no 1 pp 118ndash1282013

[27] D F Gleich ldquoPageRank beyond the webrdquo SIAM Review vol 57no 3 pp 321ndash363 2015

[28] J Wang M Li H Wang and Y Pan ldquoIdentification of essentialproteins based on edge clustering coefficientrdquo IEEE Transac-tions on Computational Biology and Bioinformatics vol 9 no4 pp 1070ndash1080 2012

[29] O Sporns ldquoContributions and challenges for network modelsin cognitive neurosciencerdquoNatureNeuroscience vol 17 pp 652ndash660 2014

16 Complexity

[30] F HaoM Chen C Zhu andM Guizani ldquoDiscovering influen-tial users inmicro-blogmarketing with influencemaximizationmechanismrdquo in Proceedings of the 2012 IEEE Global Commu-nications Conference GLOBECOM 2012 pp 470ndash474 USADecember 2012

[31] F Bodendorf and C Kaiser ldquoDetecting opinion leaders andtrends in online social networksrdquo in Proceedings of the 2ndACM Workshop on Social Web Search and Mining SWSMrsquo09Co-located with the 18th ACM International Conference onInformation and Knowledge Management CIKM 2009 pp 65ndash68 China November 2009

[32] B Xiang Q Liu E Chen H Xiong Y Zheng and Y YangldquoPageRank with priors An influence propagation perspectiverdquoin Proceedings of the 23rd International Joint Conference onArtificial Intelligence IJCAIrsquo13 pp 2740ndash2746 Beijing China2013

[33] T Zhu B Wang B Wu and C Zhu ldquoMaximizing the spread ofinfluence ranking in social networksrdquo Information Sciences vol278 pp 535ndash544 2014

[34] J Li W Peng T Li T Sun Q Li and J Xu ldquoSocial networkuser influence sense-making and dynamics predictionrdquo ExpertSystems with Applications vol 41 no 11 pp 5115ndash5124 2014

[35] C Zhou P Zhang W Zang and L Guo ldquoOn the upper boundsof spread for greedy algorithms in social network influencemaximizationrdquo IEEETransactions onKnowledge andData Engi-neering vol 27 no 10 pp 2770ndash2783 2015

[36] X Qi E Fuller R Luo and C-Q Zhang ldquoA novel centralitymethod for weighted networks based on the Kirchhoff polyno-mialrdquo Pattern Recognition Letters vol 58 pp 51ndash60 2015

[37] V Latora and M Marchiori ldquoA measure of centrality based onnetwork efficiencyrdquo New Journal of Physics vol 9 article 1882007

[38] Y Mehmood N Barbieri F Bonchi and A Ukkonen ldquoCSICommunity-level social influence analysisrdquo Lecture Notes inComputer Science (including subseries Lecture Notes in ArtificialIntelligence and Lecture Notes in Bioinformatics) Preface vol8189 no 2 pp 48ndash63 2013

[39] C S E Bale N J Mccullen T J Foxon A M Rucklidge andW F Gale ldquoModeling diffusion of energy innovations on aheterogeneous social network and approaches to integration ofreal-world datardquo Complexity vol 19 no 6 pp 83ndash94 2014

[40] P DeMeo E Ferrara D Rosaci and G M L Sarne ldquoTrust andcompactness in social network groupsrdquo IEEE Transactions onCybernetics vol 45 no 2 pp 205ndash216 2015

[41] H Liu Y Zhang H Lin J Wu Z Wu and X Zhang ldquoHowmany zombies around yourdquo in Proceedings of the 13th IEEEInternational Conference on Data Mining ICDM 2013 pp 1133ndash1138 USA December 2013

[42] Z Chu S Gianvecchio H Wang and S Jajodia ldquoDetectingautomation of Twitter accounts Are you a human bot orcyborgrdquo IEEE Transactions on Dependable and Secure Comput-ing vol 9 no 6 pp 811ndash824 2012

[43] Y Liu D Pi and L Cui ldquoMetric Learning Combining WithBoosting for User Distance Measure in Multiple Social Net-worksrdquo IEEE Access vol 5 pp 19342ndash19351 2017

[44] Q Zhang J Wu Q Zhang P Zhang G Long and C ZhangldquoDual influence embedded social recommendationrdquo WorldWide Web 2017

[45] Q Yan L Wu and L Zheng ldquoSocial network based microbloguser behavior analysisrdquo Physica A Statistical Mechanics and itsApplications vol 392 no 7 pp 1712ndash1723 2013

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Complexity

more the user A trusts user B the more influence the user Bhas on the user A Because user influence is the basis of thecommunity influence a little carelessness on the former willlead to errors on the later

Aiming to assess the community-level influence effec-tively and accurately we construct a community-level influ-ence analysis model that can assess community influenceBased on our model a community-level influence analysisalgorithm (short for CIAA) is proposed which can assessthe community influencemore effectively and accuratelyThemain idea of our model is as follows First we eliminatethe interference of zombie fans on the social influence tomake the results more accurate Then in the process ofcalculating user influence we consider the social trust anduse the random walk method to calculate the user influenceIn evaluating the userrsquos theme information the user meanwillingness is calculated by exploring the content related tothe userrsquos theme information We combine these two factors(the user influence and the user willingness to diffuse themeinformation) to calculate the user final influence Finally thecommunity-level influence is calculated by comprehensivelystudying the user final influence the social trust and rela-tionship tightness between intrausers of communities Exper-iments are conducted on a real-world dataset crawled fromSina Weibo Comparing with the state-of-the-art algorithm(the averaging user influence algorithm [18]) the results showthat our model is more effective and accurate to evaluate thecommunity-level influence

The contributions of this paper can be summarized asfollows (1) We formulate the problem of analyzing thecommunity-level influence and design a community-levelinfluence analysis model (2)CIAA a community-level influ-ence analysis algorithm based on our model is proposedwhich is effective and reliable to evaluate the communityinfluence of microbloggers from SinaWeibo (3)We conductextensive experiments to assess the performance of the pro-posed model Experimental results on the real-world datasetdemonstrate the superiority of the proposed CIAA

The rest of the paper is organized as follows In Section 2we summarize the related works In Section 3 we proposethe community-level influence analysis model and give anexample to illustrate its working principle and the CIAA isproposed In Section 4 we conduct experiments on the real-world dataset crawled from Sina Weibo and then analyze theperformance of the proposed approach Finally we state theconclusion and future work in Section 5

2 Related Works

Since Katz and Lazarsfeld [19] found that social influenceplays an important role in social life and decision-making inthe 1950s researchers in computer field have spare no effortto study the relevant problems It is found that the popularusers play an important role in adopting innovation socialpublic opinion propagation and guidance group behaviorformation and development [5] and so on

There are a great deal of research efforts to measureindividual-level influence [20 21] typically the ldquoopinionleadersrdquo Existing methods can be categorized into three

types the network structure based methods the user behav-ior based methods and the mutual information based meth-odsThenetwork structure basedmethods are degree central-ity [22] closeness centrality [23] betweenness centrality [24]eigenvector centrality [25] Katz centrality [26] PageRank[27] and clustering coefficient [28] We know that nodedegree essentially means the connection between a node andits neighbors The method based on node degree can intu-itively express this meaning and its computational cost issmaller than other methods [29] These methods are widelyused in measuring the usersrsquo influence in the social networkHowever the methods based on node degree only reflect theconnection between the users and their neighbors and cannotmeasure the usersrsquo influence in the entire social network forthe local influence of users For example based on the com-munity scale-sensitive maxdegree Hao et al [30] proposedan influential users discovering approach called CSSM whenplacing advertisements CSSM uses the degree centralityand neighborrsquos degree to evaluate nodersquos (microbloggers)influence However the algorithm does not consider thecontribution of microblogs to user influence Comparingwith the methods based on the degree the method basedon the shortest path (closeness centrality and betweennesscentrality) can measure the individual-level influence inthe entire social network Nevertheless its computationalcomplexity is higher than the degree centrality method Forexample based on text mining and social network analysisBodendorf and Kaiser [31] proposed an approach to detectopinion leaders in directed graph of user communicationrelationship It can predict tendency of network opinionleaders via closeness centrality and betweenness centralityMoreover measuring the individual-level influence by theshortest path is an ideal status and it is difficult to achievein the real-world application scenarios Besides the methodsbased on randomwalk only consider the structure character-istics of the node while ignoring the behavior characteristicsFor example Xiang et al [32] provided an understandingof PageRank and authority from an influence propagationperspective by performing random walks However theydid not consider the personal attributes to understandingof PageRank as well as the relationship between PageRankand social influence analysis Zhu et al [33] proposed anovel information diffusionmodel calledCTMC-ICMwhichintroduces the continuous-time Markov Chain theory intothe Independent Cascade Model Based on the model theyproposed a new ranking metric called SpreadRank Based oncontinuous-time Markov process Li et al [34] proposed adynamic information propagation model called IDM-CTMPto predict the influence dynamics of social network usersIDM-CTMP defined two other dynamic influence metricsand could predict the spreading coverage of a user withina given time period Zhou et al [35] established new upperbounds to significantly reduce the number of Monte-Carlosimulations in greedy-based algorithms especially at theinitial step Based on the bound they proposed a new upperbound based lazy forward algorithm for discovering the top-119896influential nodes in social networks

The aforementioned models focus only on assessingthe social influence of single individuals However a small

Complexity 3






CI (119862119894) = 119891 (119866 119862119894) (1)


Definition 1






Definition 2




Definition 3


Definition 4



Definition 5


4 Complexity

Data sources




tightness




table

Data preprocessing



u

vUI(v)

MW(u)

UI(u)

MW(u)

UI(u)

MW()

UI(v)

CS


v

v

v u

uu

u

v

MW()

Stv

＄ＣffＯtv

Sut

＄ＣffＯut

UII(C)

RT(C)















Complexity 5
















UFI (119906) = MW (119906) times UI (119906) (4)


=



(5)


6 Complexity

u1 u2

u4u5

u3

1

2

3

(a)

u1 u2

u4u5

u3

1

2

3

(b)

u1 u2

u4u5

u3

1

2

3

(c)

u1 u2

u4u5

u3

1

2

3



DiffuV119905119906119895 =


(6)



sum119905119906119895isin119879(119906)

119878V119905119906119895


sum119905119906119895isin119879(119906)

DiffuV119905119906119895 (7)

MW is calculated as

MW (V)


+ |NP (V)|num119878

(8)




119860 (1199061) = 1199062 1199065 119861 (1199061) =

119908 (1199062) =12

119908 (1199065) =14

MW (1199061)


(9)


119860 (1199062) = 1199061 1199064 119861 (1199062) = 119908 (1199062) = 1

119908 (1199064) =13


3+ 13 =

118

(10)

Complexity 7


NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13


3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 3






CI (119862119894) = 119891 (119866 119862119894) (1)


Definition 1






Definition 2




Definition 3


Definition 4



Definition 5


4 Complexity

Data sources




tightness




table

Data preprocessing



u

vUI(v)

MW(u)

UI(u)

MW(u)

UI(u)

MW()

UI(v)

CS


v

v

v u

uu

u

v

MW()

Stv

＄ＣffＯtv

Sut

＄ＣffＯut

UII(C)

RT(C)















Complexity 5
















UFI (119906) = MW (119906) times UI (119906) (4)


=



(5)


6 Complexity

u1 u2

u4u5

u3

1

2

3

(a)

u1 u2

u4u5

u3

1

2

3

(b)

u1 u2

u4u5

u3

1

2

3

(c)

u1 u2

u4u5

u3

1

2

3



DiffuV119905119906119895 =


(6)



sum119905119906119895isin119879(119906)

119878V119905119906119895


sum119905119906119895isin119879(119906)

DiffuV119905119906119895 (7)

MW is calculated as

MW (V)


+ |NP (V)|num119878

(8)




119860 (1199061) = 1199062 1199065 119861 (1199061) =

119908 (1199062) =12

119908 (1199065) =14

MW (1199061)


(9)


119860 (1199062) = 1199061 1199064 119861 (1199062) = 119908 (1199062) = 1

119908 (1199064) =13


3+ 13 =

118

(10)

Complexity 7


NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13


3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




4 Complexity

Data sources




tightness




table

Data preprocessing



u

vUI(v)

MW(u)

UI(u)

MW(u)

UI(u)

MW()

UI(v)

CS


v

v

v u

uu

u

v

MW()

Stv

＄ＣffＯtv

Sut

＄ＣffＯut

UII(C)

RT(C)















Complexity 5
















UFI (119906) = MW (119906) times UI (119906) (4)


=



(5)


6 Complexity

u1 u2

u4u5

u3

1

2

3

(a)

u1 u2

u4u5

u3

1

2

3

(b)

u1 u2

u4u5

u3

1

2

3

(c)

u1 u2

u4u5

u3

1

2

3



DiffuV119905119906119895 =


(6)



sum119905119906119895isin119879(119906)

119878V119905119906119895


sum119905119906119895isin119879(119906)

DiffuV119905119906119895 (7)

MW is calculated as

MW (V)


+ |NP (V)|num119878

(8)




119860 (1199061) = 1199062 1199065 119861 (1199061) =

119908 (1199062) =12

119908 (1199065) =14

MW (1199061)


(9)


119860 (1199062) = 1199061 1199064 119861 (1199062) = 119908 (1199062) = 1

119908 (1199064) =13


3+ 13 =

118

(10)

Complexity 7


NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13


3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 5
















UFI (119906) = MW (119906) times UI (119906) (4)


=



(5)


6 Complexity

u1 u2

u4u5

u3

1

2

3

(a)

u1 u2

u4u5

u3

1

2

3

(b)

u1 u2

u4u5

u3

1

2

3

(c)

u1 u2

u4u5

u3

1

2

3



DiffuV119905119906119895 =


(6)



sum119905119906119895isin119879(119906)

119878V119905119906119895


sum119905119906119895isin119879(119906)

DiffuV119905119906119895 (7)

MW is calculated as

MW (V)


+ |NP (V)|num119878

(8)




119860 (1199061) = 1199062 1199065 119861 (1199061) =

119908 (1199062) =12

119908 (1199065) =14

MW (1199061)


(9)


119860 (1199062) = 1199061 1199064 119861 (1199062) = 119908 (1199062) = 1

119908 (1199064) =13


3+ 13 =

118

(10)

Complexity 7


NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13


3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




6 Complexity

u1 u2

u4u5

u3

1

2

3

(a)

u1 u2

u4u5

u3

1

2

3

(b)

u1 u2

u4u5

u3

1

2

3

(c)

u1 u2

u4u5

u3

1

2

3



DiffuV119905119906119895 =


(6)



sum119905119906119895isin119879(119906)

119878V119905119906119895


sum119905119906119895isin119879(119906)

DiffuV119905119906119895 (7)

MW is calculated as

MW (V)


+ |NP (V)|num119878

(8)




119860 (1199061) = 1199062 1199065 119861 (1199061) =

119908 (1199062) =12

119908 (1199065) =14

MW (1199061)


(9)


119860 (1199062) = 1199061 1199064 119861 (1199062) = 119908 (1199062) = 1

119908 (1199064) =13


3+ 13 =

118

(10)

Complexity 7


NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13


3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 7


NDTI1199063 = 0 + 0 + 0 = 0

NRTI1199063 = 0 + 0 + 1 = 1

MW (1199063) =06 times 0 + 04 times 0

3 + 0 = 0

NDTI1199064 = 1 + 1 + 1 = 3

NRTI1199064 = 1 + 1 + 1 = 3

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) = 1

119860 (1199064) = 1199061 1199062

119861 (1199064) = V2

119908 (1199061) =13

119908 (1199062) =12

119908 (V2) = 1

119860 (1199064) = 1199062

119861 (1199064) =

119908 (1199062) =13


3 + 0 = 2865

NDTI1199065 = 0 + 1 + 1 = 2

NRTI1199065 = 1 + 1 + 1 = 3

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199062) =13

119908 (1199064) =13

119860 (1199065) = 1199061

119861 (1199065) =

119908 (1199061) =13

119860 (1199065) = 1199062

119861 (1199065) = V2

8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




8 Complexity

119908 (1199062) =13

119908 (V2) = 1


3 + 0 = 49 (11)



DTV119906 =RU (119906)

outdegree (V)


(12)


RU (1199061) =01 + 01 + 01 + 01

4 + 1 = 008

In (1199061) = 1199062 1199064 1199065 V1

DT1199062 1199061 =0082 = 004

DT1199063 1199061 =0080 (written as 0)

DT1199064 1199061 =0082 = 004

DT1199065 1199061 =0084 = 002

DTV1 1199061 =0082 = 004

DTV2 1199061 =0081 = 008

DTV3 1199061 =0080 (written as 0)

(13)


DI119906V =119868 (119906 larr V)

outdegree (V)


(14)



119868 (1199061 larr997888 1199062) =22 = 1

119868 (1199061 larr997888 1199063) =01 = 0

119868 (1199061 larr997888 1199064) =23 = 0667

119868 (1199061 larr997888 1199065) =23 = 0667

119868 (1199061 larr997888 V1) =23 = 0667

119868 (1199061 larr997888 V2) =23 = 0667

119868 (1199061 larr997888 1199063) =20 (written as 0)

(15)


DI11990611199062 =12 = 05

DI11990611199063 =00 is 0

DI11990611199064 =06672 = 0334

DI11990611199065 =06675 = 0133

DI1199061V1 =06672 = 0334

DI1199061V2 =11 = 1


(16)


ITV119906 =RU (119906)minV119906

(17)

Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 9



IT11990621199061 =0081 = 008

IT11990631199061 =0080 (written as 0)

IT11990641199061 =0081 = 008

IT11990651199061 =0081 = 008

ITV11199061 =0081 = 008

ITV21199061 =0082 = 004

ITV31199061 =0080 (written as 0)

(18)


II119906V =119868 (119906 larr V)minV119906


(19)


II11990611199062 =11 = 1

II11990611199063 =00 (written as 0)

II11990611199064 =06671 = 0667

II11990611199065 =06671 = 0667

II1199061V1 =06671 = 0667

II1199061V2 =12 = 05


(20)











UI (1199061)


5= 0133

(24)




UII (119862119894) = sum119906isin119862119881(119906)

UFI (119906) (25)



CS (119862119894) =1003816100381610038161003816119862119881 (119862119894)

1003816100381610038161003816max (119881) (26)


10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




10 Complexity







119862119881 (119862119894) (27)



times RT (119862119894) (28)



4 Experiments










Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 11

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(a)

0

1000

2000

3000

4000

Cou

nt

20 40 60 80 1000Value

(b)







43 Results








12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




12 Complexity

Table6Th

reeu

sersetsfor

elim

inatingzombiefansTh

eboxes

representzom

biefans

NUI

NAU

NUF

511lowast


320lowast


226lowast


257lowast


122lowast


384lowast


348lowast


214lowast


522lowast


267lowast


377lowast


506lowast


508lowast


203lowast


569lowast


569lowast


514lowast


565lowast


209lowast


314lowast


551lowast


535lowast


540lowast


512lowast


512lowast


314lowast


553lowast


535lowast


260lowast


564lowast


540lowast


272lowast


345lowast


345lowast


560lowast


550lowast


569lowast


299lowast


326lowast


541lowast


532lowast


553lowast


553lowast


362lowast


557lowast


519lowast


255lowast


546lowast


236lowast


508lowast


241lowast


241lowast


169lowast


528lowast


174lowast


295lowast


366lowast


124lowast


567lowast


538lowast


538lowast


568lowast


551lowast


176lowast


312lowast


140lowast


541lowast


514lowast


237lowast


237lowast


293lowast


295lowast


381lowast


312lowast


357lowast


365lowast


561lowast


267lowast


267lowast


512lowast


549lowast


522lowast


275lowast


547lowast


557lowast


219lowast


516lowast


516lowast


531lowast


108lowast


180lowast


272lowast


558lowast


562lowast


554lowast


216lowast


535lowast


540lowast


563lowast


508lowast


393lowast


520lowast


295lowast


519lowast


395lowast


395lowast


508lowast


560lowast


267lowast


325lowast


564lowast


217lowast


395lowast


531lowast


531lowast


514lowast


320lowast


194lowast


299lowast


291lowast


155lowast


240lowast


531lowast


531lowast


503lowast


553lowast


519lowast


398lowast


564lowast


535lowast


398lowast


518lowast


518lowast


217lowast


365lowast


213lowast


526lowast


564lowast


563lowast


569lowast


540lowast


540lowast


368lowast


565lowast


299lowast


297lowast


551lowast


523lowast


308lowast


393lowast


393lowast


241lowast


561lowast


365lowast


506lowast


269lowast


516lowast


553lowast


107lowast


260lowast


301lowast


524lowast


263lowast


327lowast


377lowast


562lowast


315lowast


553lowast


553lowast


546lowast


315lowast


505lowast


184lowast


349lowast


286lowast


199lowast


282lowast


282lowast


398lowast


530lowast


281lowast


293lowast


387lowast


537lowast


564lowast


387lowast


506lowast


175lowast


558lowast


249lowast


530lowast


202lowast


266lowast


531lowast


558lowast


558lowast


559lowast


557lowast


217lowast


206lowast


561lowast


564lowast


563lowast


381lowast


381lowast


559lowast


565lowast


393lowast


227lowast


562lowast


554lowast


190lowast


377lowast


377lowast


521lowast


564lowast


367lowast


324lowast


282lowast


181lowast


190lowast


532lowast


532lowast


564lowast


535lowast


354lowast


246lowast


524lowast


550lowast


163lowast


326lowast


326lowast


561lowast


558lowast


202lowast


107lowast


524lowast


558lowast


567lowast


183lowast


183lowast


533lowast


527lowast


140lowast


259lowast


546lowast


562lowast


548lowast


297lowast


107lowast


536lowast


537lowast


206lowast


395lowast


554lowast


558lowast


562lowast


215lowast


215lowast


384lowast


528lowast


240lowast


371lowast


508lowast


219lowast


186lowast


373lowast


373lowast


207lowast


297lowast


292lowast


177lowast


565lowast


356lowast


532lowast


331lowast


331lowast


361lowast


535lowast


289lowast


321lowast


548lowast


557lowast


329lowast


372lowast


372lowast


561lowast


539lowast


378lowast


299lowast


376lowast


363lowast


558lowast


385lowast


385lowast


562lowast


562lowast


280lowast


315lowast


557lowast


559lowast


327lowast


564lowast


558lowast


528lowast


558lowast


386lowast


562lowast


293lowast


551lowast


554lowast


375lowast


375lowast


387lowast


316lowast


219lowast


346lowast


558lowast


185lowast


362lowast


565lowast


569lowast


173lowast


560lowast


166lowast


562lowast


352lowast


122lowast


292lowast


387lowast


387lowast


393lowast


288lowast


248lowast


521lowast


561lowast


531lowast


558lowast


538lowast


538lowast


565lowast


549lowast


246lowast


257lowast


531lowast


557lowast


531lowast


558lowast


Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 13



UFI withzombie fans

The actualrankings




fansNumber of

blogsAuthenticated








fansNumber of

blogs

Microblog-fans


Use

r 1

Use

r 2

Use

r 3

Use

r 4

Use

r 5

Use

r 6

Use

r 7

Use

r 8

Use

r 9

Use

r 10

Num_blogsNum_fans

Microblogger

0

1000

2000

3000

4000

5000N

umbe

r




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




14 Complexity




UFIMicroblog-fans


00

02

04

06

08

Accu

racy

(01 09)(025 085)(03 05)(05 05)(04 08)






CIAAAI

0

20

60

40

80

100

120

0

20

60

40

80

100

120

Com

mun

ity-le

vel i

nflue

nce

(040

4)

(010

4)

(060

3)

(050

3)

(030

3)

(070

2)

(050

2)

(030

2)

(010

2)

(00

)



5 Conclusion


Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 15



Acknowledgments


References































16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




16 Complexity
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Mining Community-Level Influence in Microblogging Network...

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Transcript of Mining Community-Level Influence in Microblogging Network...