[IEEE 2012 Third International Conference on Services in Emerging Markets (ICSEM) - Mysore, India...

SOCIAL NETWORK EVOLUTION: A CASE STUDY OF UK DIRECTORS

Azar Shahgholian, Babis Theodoulidis, Uttam Bansal Centre for Service Research

Manchester Business School The University of Manchester

Booth Street East, Manchester M13 9ss, United Kingdom

[email protected]; [email protected]; [email protected]

Abstract— Social network can be seen as a dynamic process of creating and breaking down relationships among network members. The network evolution is of major interest to researchers in this area due to discovering patterns of structural changes in the network. In this study, the evolution of UK directors’ social network is examined. The study carried out on a systematic analysis of network properties and evolution factors. The network properties include shortest path, number of shared affiliations, cyclic closure and triadic closure property. It is observed that directors who are not connected directly in specific year and have only a single intermediary between them are more likely to form a connection in the future than the directors with two intermediaries. Moreover, the number of mutual friends increases the chances of a connection between the directors in future.

Keywords- Social network evolution, Network of UK directors, Dynamic social network analysis, Data mining, Graph theory

I. INTRODUCTION

Social networks have been a key research area in recent years, because they can help to understand the behaviour of their members, social influence, decision making and build credibility for companies [1]. In reference [2] network was introduced as a set of nodes and a set of ties representing some relationships, or lack of relationships, between the nodes. The study of networks based on several measures to understand the network structure by description, visualisation, and (statistical) modelling is termed as Social network analysis [3] .

The analysis of social network is of interest to many fields such as sociology [4] and recommendation system [5]. In addition, research in social network analysis has highlighted several significant management issues [6]. In all study fields, dynamic networks have been considered as an interesting phenomenon. The main reason is that in static analysis the time of interactions is not considered. Therefore, the opportunity to capture the patterns in dynamic networks is not available. Indeed, most networks are dynamic as they tend to evolve gradually, due to frequent changes in the activities and interactions of their members [7]. More specifically, social networks evolve over time with the formation and deletion of connection between members of the network as well as introducing new members and

removing old ones. The shaping of a social network is a complex process and there are many factors and reasons that lead to the formation and breaking up of connections. Hence, an important area of the analysis is to examine how the structure of a social network evolves and the characteristics of the process involved.

In this paper, we have analysed the social network of directors of UK companies based on the BoardEx dataset [8], in which their current and past employment are recorded over a period of time and matched with the associated companies, education background and other professional activities. In this study, we concentrate only on the current employment network of UK directors. In addition to network connectedness, the various types of connections are also taken into account to analyse the difference of their impact on the network properties. The analysis is carried out on the evolution of network over a period of twelve years in order to determine the consistency of the results over time.

The results of the analysis reported in the paper confirm that the empirical probability of link formation between various directors over time is driven by the proximity between them. It is observed that the unconnected directors who have only a single intermediary between them are more likely to form a connection in the future than the directors with two intermediaries. Moreover, the number of mutual friends increases the chance of a connection between the directors in future.

The paper is organised as follows. In section II, we discuss the related work on the theoretical and experimental analysis of social networks and in particular social networks of directors. In section III, our proposed method including dataset and definition of social network of UK directors are introduced, followed by analysis and results in section IV. Finally, section V concludes the paper.

II. RELATED WORK

One of the important aspects of social network analysis is to study the evolution of network. Social networks evolve over time with the formation and deletion of connections between members of the network as well as introduction of new members and removal of old ones. Understanding the patterns governing the evolution of social networks is very meaningful. There are several research papers that provide a variety of insights on the evolution of networks. For

2012 Third International Conference on Services in Emerging Markets

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DOI 10.1109/ICSEM.2012.22

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instance, [9] argues that individuals form and sever links over time and connect themselves to other individuals based on the improvement that the resulting network offers them in relation to the current network. The information which is exchanged between the individuals within a network also depends on the structure of the network. That information can be of any type, some elementary information like an invitation to a party and something more significant like information about job opportunity [10] [11] [12], literacy [13] , consumer products [14] , or even information regarding the returns to crime [15]. In [9], a model is proposed in which network formation was used as a dynamic process and they based it on the assumption that individuals form and sever links based on the improvement that the resulting network offers them. One way to model the structural changes in dynamic networks is to convert an evolving network into static graphs at different snapshots [16]. Dynamic analysis of social network provides various insights into understanding the structure of the complex networks, detecting a drastic change in the interaction patterns and making prediction about the future trends of the network [17].

Along with the mentioned factors, there can be several other factors that can drive the network evolution. There are some empirical evidence that the network evolution can be driven by centrality, where individuals or nodes in a network with higher centrality are more likely to form or receive links [18][19][20]. The model presented by [20] assumes that nodes create a link to the one with the highest centrality in its second-order neighbourhood, however for their network evolution it concludes that it is independent of the exact measure of centrality, thus centrality does not drive how the connections forms between the nodes over time.

In reference [21], it is mentioned that individuals make link to new individuals who are friends of friends. This process known as triadic closure, can be explained more clearly as if ‘A’ directs a tie to ‘B’, and ‘B’ directs a tie to ‘C’, then ‘A’ also directs a tie to ‘C’[22][23]. The information they seek may be trivial but a mutual connection between them helps to extend a link towards each other. In reference [21]; network of students is used to carry out an empirical analysis of their evolving social network based on the email communication that signifies the connection between the students. The paper tries to find out through evaluating several network measures how the new links are formed between the individuals. Link formation was observed for individuals that have one, two or more connections between them and the percentage of new connections that is formed between these individuals was calculated. The paper finds out that there is one-third chance of forming a link between individuals who are separated by two intermediaries as compared to individuals with only one intermediary. Thus, increasing distance between two strangers lowers the probability of making a new connection between them in the future. It also finds out that if two strangers have high number of mutual acquaintances then the probability of making a connection is higher as compared to the individuals with less number of mutual acquaintances. Along with that, the stronger bond with their mutual

acquaintance also drives them to form a connection between them in future. In [21], it was concluded that the findings observed by their research on the formation are links between two nodes over time are generic and they can be applied to a variety of context to check any network specific behaviour.

There have been several researches done in the past that analysed the network of directors, e.g. For example, there has been a research to evaluate how the relationship of directors affect critical decisions for the firms [24], the effect on the compensation of CEO [25] [26] and the impact of board interlock networks (boards are connected by interlocked directors–individuals who are officers and/or directors at two or more firms) on directorship market outcomes and firm values [27]. These researches will be used as references for the creation of network of directors and then the evolution of network is studied over a period of time.

According to previous research considering the impact of social network between companies and their directors, it is proved that forming and removing relationships between directors have direct effects on many aspects of companies. Therefore, investigating the evolution of their network over time could be helpful to understand the structures of the complex network of directors as well as detecting the hidden pattern among their interactions. To the best of our knowledge, there is no research that has investigated the evolution of this network over time. In this research, the results will be compared with the results of [21].

III. PROPOSED METHOD

As mentioned earlier, the objective of the research is to study the evolution of social networks of UK company executives. This study is based on the dataset for directors from the UK region which is provided by BoardEx. In this paper, we based our research on two stages. In first stage, we build social network between directors by using BoardEx dataset and then, in second stage, the evolving social network of directors over past 12 years is analysed to examine if there is a pattern of how directors are motivated towards making new links in their network over time.

A. Dataset BoardEx dataset mainly keeps information of directors

from USA and Europe region that work in publicly quoted companies and major private entities at board and executive management levels. The information is updated on a regular basis, including keeping track of any changes in the employments of existing individuals in the database and adding of information about new individuals in the network and the de-listed companies from year 1999 to 2011. The information includes in-depth profiles such as academic qualifications, current and past job positions, membership to professional and other bodies, peer esteem indicators such as awards and honorary positions, etc. In this study we have focused on UK directors from 2000 to 2011.awards and honorary positions, etc. In this study we have focused on UK directors from 2000 to 2011.

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B. Building social networks of directors Based on the BoardEx dataset, it is possible to build the

social networks of directors based on their current and past job positions, education background, their membership in other activities and then overall social network index. However, in this paper, we concentrated on current employment network. We believe that the assumptions which are used to create relationships between directors have direct effects on further analysis. Therefore, we define “Current Employment Network “as follow:

“If two directors are currently working on the board of a same S&P company or are currently associated with a same organisation (Non S&P companies) and also play an active role in that organisation like “Trustee”, “Chairman” or “Advisor” and not just a member or fellow, then we assume there is a connection between these two directors and a network is defined as Current employment network”.

The pre-processing and generation of links for each type of networks have been carried out using PASW Modeller [16]. The links are obtained for each network for each year from 2000 to 2011 and then have been processed through NodeXL (http://nodexl.codeplex.com) by removing any duplicates nodes and creation of final data files that can be used through NetworkX [13] for calculating various network metrics.

C. Analysing network evolution of UK directors This research carries out the analysis majorly based on

identifying the formation of new links between a set of directors over years. In order to model the structural changes in dynamic networks, we follow the model proposed by [3] and convert an evolving network into static graphs at different snapshots. Our approach is using yearly basis snapshots of network from 2000 to 2011. The provided method is capturing the pattern of changes between two consecutive snapshots.

The motivation of current study is based on [9] [25] which is stated that “if two people in a social network have a friend in common, then there is an increased likelihood that they will become friends themselves at some point in the future”.

In order to apply this hypothesis on our study, two measures are calculated for all the connected pair of directors in the network: Shortest Path Length Dd1-d2 – the shortest path length between two directors in the network [9] and Number of shared affiliations Sd1-d2 – the number of mutual friends of any two pair of directors with shortest path length equals to two [9]. These two measures are necessary to find out common friends between each pairs in the specific time. By identifying the new links that appear over time, the following set of network measures will be calculated for the network:

• Cyclic closure bias • Triadic closure bias based on mutual acquaintance. The description and significance of these metrics with

respect to our social network is as follows:

Figure 1. Cyclic closure property for directors which are at a distance 2

apart. 1) Cyclic Closure Bias: For any specified value of Dd1-d2,

the cyclic closure bias is defined as the empirical probability that two previously disconnected director d1 and d2 who are at a distance Dd1-d2 apart will initiate a new connection as shown in Figure 1. This property is generalised form of Triadic closure property for any social network which states that “if two directors in their current employment social network have an intermediary in common, then there is an increased likelihood that they form connection(s) between themselves at some point in the future” [22] [28].

Regarding the triadic closure property, these two unconnected people are at a distance two apart from each other, however this model evaluate the probability of closure for directors who are at distance two, three and four apart to analyse the social network of directors for any pattern of closure based on distance. This measure will be evaluated for Current Employment network to help us evaluate the current trend of the employment history of directors.

2) Triadic closure bias based on mutual acquaintance: This measure is based on the shared affiliations between any pair of directors who are at distance 2 (Dd1-d2 = 2) apart. As there can be more than one path between any two directors with same length, it implies that directors who are at a distance 2 can have more than one mutual connection/friend between them. This measure finds the empirical probability of triadic closure for any pair of directors with N number of mutual friends as shown in Figure 2, where N = 1, 2, 3, 4, >=5.

The results for different number of mutual friends will be used to analyse the effect of number of connections on the triadic closure bias in the social network of directors.

Regarding to the above discussion, two hypotheses are established in order to examine the probability of making new connection between pair of directors who are not connected directly in specific year. With respect to the shortest path distance and number of shared affiliations, two hypotheses are presented as follow:

a) Hypothesis 1: The longer the shortest distance path between two directors who are not connected directly in

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specific year (yi), the lower the probability of making a new connection between them in consecutive year (yi+1).

Figure 2. Triadic closure property for directors with 2 and 3 mutual friends.

b) Hypothesis 2: The higher the number of mutual connections between two directors who are not connected directly in specific year (yi), the higher the probability of making a new connection between them in consecutive year (yi+1).

IV. ANALYSIS AND RESULTS

A. Network evaluation based on Cyclic Closure Bias This section presents the results and evaluation of cyclic

closure for Current Employment Network of directors for two different values of shortest distance length Dd1-d2 between any two pair of directors. Hypothesis 1 discussed in Section 3.3 will be tested.

1) Results Table 1 provides the network evaluation for the cyclic

closure bias Current Employment Network. For each row in the table, the first column Yi represents the year for which the network is evaluated for the pair of directors with shortest path distance length of 2 and 3. The second column is the next year Yi+1, for which the same net-work is evaluated for the new links formed between the directors. The values P2 and P3 represent the total number of director pair with shortest path distance of length 2 and 3 respectively in the year Yi. The values C2 and C3 represent the total number of pairs of directors from P2 and P3 that made a new connection in year Yi+1.

The empirical probability of the directors connected for each year is represented by F2 and F3 for shortest distance path length 2 and 3 respectively. The last column ∆F shows the likeliness of F2 over F3 for each year.

2) Analysis and Interpretation Figure 3 shows a chart that depicts the empirical

probability of making new connections between the pair of directors with shortest distance path length of 2 and 3 from year 2001 to 2011.

As it can be observed from the figure the probability of new link formation for shorter distance (i.e. for Dd1-d2 = 2) is higher throughout the period of 12 years. The last column in Table 1 also shows that likelihood of directors who are separated by two intermediaries (Dd1-d2 = 3) is 4 to 11 times

less than the directors with just one intermediary (Dd1-d2 = 2) from year 2001 to 2011.

Since, the empirical probability of directors with longer distance is lower than that of shorter distance, there is a probability that the Hypothesis 1 established is true. Our result confirm the result presented in [21]. Thus, we can argue that “the longer the shortest distance path length between two unconnected directors; the lower the probability of making a new connection between them in time, as stated in hypothesis 1”.

B. Network evaluation based on Shared Affiliation Bias Based on the discussion of shared affiliations bias for

directors who are not connected directly in Section 3.3, this section presents the results and evaluation for Current Employment Network for different values of mutual friends between any two pair of directors separated by one intermediary (Dd1-d2 = 2).

1) Results Table 2 provides the network evaluation for shared

affiliation bias for Current Employment Network. Similarly, like table 1 the first column Yi in table 2

represents the year for which the network is evaluated for the pair of directors with a number of shared affiliations or mutual friends. The second column is the next year Yi+1, for which each network is evaluated for the new links formed between the directors. The values P1, P2, P3, P4 and P5 represent the total number of pair directors with 1, 2, 3, 4 and >=5 mutual friends respectively in the year Yi. The values from C1 to C5 represent the total number of pairs of directors from P1 to P5 that got connected in next year Yi+1. The empirical probability of the directors connected for each year is represented by F1, F2, F3, F4 and F5 for 1, 2, 3, 4 and those with 5 or more mutual friends respectively.

2) Analysis and Interpretation Figure 4 shows a scattered chart for the analysis of

Current Employment. The figures depicts the empirical probability of making new connections between the pair of directors with varying number of mutual friends from 1 to 5 or more than 5 and the results are obtained for different years to show the variations with time.

It is observed in figure 4, that the empirical probability of making new connections for any year tends to increase with increasing the number of mutual connections between any two unconnected directors. However, it was noticed that for year 2003 and 2007, there is slight change in the behaviour when we increase the number of mutual friends from 3 to 4 and 4 to 5 respectively. It is also noticed that the probability for different values of shared affiliations varies considerably for different years with no defined flow. This can be attributed to the fact that in Current Employment networks and the past connections of directors of directors are not considered which might play a vital role in increasing the number of mutual connections between any pair of directors.

Since, the empirical probability of directors making new connection increases with the increase in the number of mutual friends, one can argue that the Hypothesis 2 established is true. This result is also similar to the one reported in [21] although it relates to a different domain.

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Thus, we can accept that “The higher the number of mutual connections between two unconnected directors, the Higher the probability of making a new connection between them as stated in hypothesis 2”.

V. CONCLUSIONS

In this paper, the network of UK directors is created based on the BoardEx dataset. The evolution of the network of directors is analysed to explore the role of their position and connectedness with other directors. The evaluation of networks based on the link formation provided two conclusions. Firstly, the probability of any two unconnected directors in a network with just one intermediary to form a new link is 4 to 11 times higher than directors with two intermediaries. Secondly, the empirical probability of new link formation between two unconnected directors increases in the number of mutual acquaintances. It might be interpreted from the results that the director joins new company because they already have some connection with the board members of that company or these changes can help companies to investigate the impact of the connection between their board members with other companies in their decision making. The connection could be a friend of a friend already working with that company. Evidently, the higher number of mutual friends and the strong tie with those mutual friends is also one of the criteria that lead to the formation of a new connection with a company.

For the future work, we plan to extend our experiment on other type of connection between directors; i.e. past employment, education background, other activities and overall social network index; to discover the most effective type of links in network evolution. In addition, the evolution of directors can be used to investigate the evolution of the network of companies over time i.e. how links between companies relate to the social network of their directors and how they evolve.

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Table 1. Cyclic Closure Bias evaluation for Current Employment Network

Yi Yi+1

Dd1-d2 = 2 Dd1-d2 = 3 ∆F=

F2/F3 Possible Pairs in

(Yi, P2) Pairs

connected in (Yi+1, C2)

Fraction of Pairs connected F2= C2/P2

Possible Pairs in (Yi, P3)

Pairs connected in

(Yi+1, C3)

Fraction of Pairs Connected F3 =C3/P3

2000 2001 188596 392 0.002079 1079744 492 0.000456 4.56

2001 2002 193598 311 0.001606 1081479 464 0.000429 3.74

2002 2003 189562 283 0.001493 1018969 459 0.00045 3.31

2003 2004 185576 293 0.001579 960966 468 0.000487 3.24

2004 2005 194253 411 0.002116 995527 513 0.000515 4.11

2005 2006 199520 428 0.002145 987645 529 0.000536 4.01

2006 2007 193527 420 0.00217 914757 532 0.000582 3.73

2007 2008 181428 731 0.004029 795818 603 0.000758 5.32

2008 2009 166785 1197 0.007177 727642 980 0.001347 5.33

2009 2010 165203 1802 0.010908 671986 711 0.001058 10.31

2010 2011 175867 1456 0.008279 815100 689 0.000845 9.79

0

0.005

0.01

0.015

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

YearEmpirical probability of connection for D = 2Empirical probability of connection for D = 3

Figure 3. Result analysis for cyclic closure bias for Current Employment network

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Table 2. Shared Affiliations evaluation for Current Employment Network

Yi Yi+1

Mutual Friends = 1 Mutual Friends = 2


Pairs connected in Year Yi+1, C1

Fraction of Pairs connected F1 = C1/P1




2000 2001 176073 279 0.00158 9543 72 0.00754

2001 2002 182567 253 0.00139 8329 43 0.00516 2002 2003 180487 192 0.00106 6421 44 0.00685

2003 2004 177235 229 0.00129 6012 40 0.00665 2004 2005 185508 281 0.00151 6048 75 0.01240

2005 2006 190208 261 0.00137 5952 64 0.01075 2006 2007 184213 331 0.00180 6698 55 0.00821

2007 2008 170951 490 0.00287 7853 196 0.02496 2008 2009 157083 839 0.00534 6488 116 0.01788

2009 2010 144996 805 0.00555 6878 145 0.02108 2010 2011 164964 708 0.00429 7818 503 0.06434

Yi Yi+1

Mutual Friends = 3 Mutual Friends = 4







2000 2001 1230 5 0.00407 439 8 0.01822

2001 2002 1031 9 0.00873 411 1 0.00243 2002 2003 1016 27 0.02657 449 6 0.01336

2003 2004 706 3 0.00425 513 4 0.00780 2004 2005 901 14 0.01554 703 15 0.02134

2005 2006 1418 17 0.01199 452 6 0.01327 2006 2007 1157 10 0.00864 484 9 0.01860

2007 2008 1299 29 0.02232 521 12 0.02303 2008 2009 982 14 0.01426 366 16 0.04372

2009 2010 1042 29 0.02783 349 11 0.03152 2010 2011 1299 101 0.07775 177 14 0.07910

Yi Yi+1

Mutual Friends >= 5




2000 2001 1311 28 0.02136

2001 2003 1260 5 0.00397 2002 2003 1189 14 0.01177

2003 2004 1110 17 0.01532 2004 2005 1093 26 0.02379

2005 2006 1490 81 0.05436

2006 2007 975 15 0.01538

2007 2008 804 4 0.00498

2008 2009 1866 212 0.11361

2009 2010 11938 814 0.06819

2010 2011 1609 130 0.08080

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Figure 4. Result analysis for shared affiliations bias for Current Employment Network.

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