Large Human Communication Networks Patterns and a Utility-Driven Generator
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Transcript of Large Human Communication Networks Patterns and a Utility-Driven Generator
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Du, Faloutsos, Wang, Akoglu
Large Human Communication NetworksPatterns and a Utility-Driven Generator
Nan Du1,2, Christos Faloutsos2, Bai Wang1, Leman Akoglu2
1Beijing University of Posts and Telecommunications,2Carnegie Mellon University
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Human Communication Network
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Clique
• Real social networks have many triangles. What about the cliques ?
• Clique is a complete subgraph, which describes a group of closelyrelated friends.
• If a clique can not be contained by any largerclique, it is called the maximal clique.
• {0,1,2}, {0,1,3}, {1,2,3}{2,3,4}, {0,1,2,3} are cliques;{0,1,2,3} and {2,3,4} are the maximal cliques.
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Goals
• Q1: Find properties that cliques hold in real social networks– Q1.1: How does the number of our social
circles (maximal cliques) relate to our degree ?
– Q1.2: How do people participate into cliques ?– Q1.3: What patterns do the edge weights
follow in triangles ?• Q2: How can we produce an intuitive emergent
graph generator to reflect human’s natural communication behaviors ?
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Outline
• Motivation• Q1: Observations• Q2: Utility-Driven Model• Conclusion• Related Work
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Data Description
• 3 typical mobile services (S1,S2,S3) (eg., phone, SMS, IM, e-mail, etc.)
• 2 geographic locations, 5 consecutive time periods (T1~T5)
• Up to 1M records. Each record is represented as <callerID, calleeID, time>
3
11G is the graph of service type S1
at time T1
ST
Multiple interactions are represented as edge weight.
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Observation 1
Question 1.1 : How does the number of our social circles (maximal cliques) relate to our degree d i
C
avg
di
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Observation 1 Clique-Degree Power-Law
idg iavC d
is the average number of maximal cliques that nodeswith degree participate in.
idavg
i
C
d
1 8 2 2 is the power law exponent
[ . , . ] for S1~S3
More friends, even more social circles !
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Observation 1 Clique-Degree Power-Law
• Outlier Detection
Spammer-like!
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Observation 2
Question 1.2 : What is the distribution of clique participation ?
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Observation 2 Clique-Participation Law
Vclique
is the set of nodes whose number of maximal cliques equals to n
clique.
3 31 1 73[ . , . ] for S1~S3cp
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Observation 3
Question1.3 : Nodes in a triangle are topologically equivalent. Will they also give equal number of phone calls to each other ?
Max
Wei
ght M
in Weight
Mid Weight
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Observation 3 Triangle Weight Law
MM iax dWWeig eiht ght
MM iax nWWeig eiht ght
MM iid nWWeig eiht ght
0 5 0 7[ . , . ] for S1~S3
0 4 0 6[ . , . ] for S1~S3
0 7 0 8[ . , . ] for S1~S3
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Outline
• Motivation• Q1: Observations• Q2: Utility-Driven Model• Conclusion• Related Work
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Goals of Utility-Driven Model
• Intuitive model to reflect human natural behaviors– Instead of using randomness, people choose their
contacts to maximize some utility.• Emergent Model
– Nodes can only access to their local information, but the network structure will still emerge from their collective interactions
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Goals of Utility-Driven Model – cnt’d
• Mimic both of the known patterns and the new patterns– Heavy-tailed degree/node weight distribution– Heavy-tailed connected components distribution– Clique-Degree Power-Law– Clique-Participation Law– Triangle Weight Law
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PaC Model
• People can benefit from calling each other.• A Pay and Call game = PaC Model• The payoffs are measured as “emotional
dollars”.
agent
Friendliness Value Fi∈(0,1)
1iF 0iF
initial capital
probability to stay in the gameLP
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Outline of Agent Behavior
• Step 1: decide to stay (PL)
• Step 2: if stay, call the most profitable person(s)– Existing friend (‘exploit’)– Stranger (‘explore’) or ask
for recommendation (if available) to maximize benefits
Exponential lifetime
Rich get richer
Closing Triangle
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PaC model - details
Benefit of a phonecall between agent ai and aj
• • Benefit drops with length of each phonecall
(‘saturation’, diminishing returns in economics)
Cost of a phonecall between agent ai and aj
• Start-up cost (Cini)
• Cost-per-minute (Cpm)
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Benefit = Fi ×Fj
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PaC Model - formulas
benefits = Fi ×Fj × (1+ + 2 + ... +m−1)∑
1
1
m
i jF F
payoffs =benefits−Cini −m×Cpm
•
–
• – – –
is the initiation costiniC
is the per-minute ratepmC is the duration of a conversationm
(diminishing returns in economics)
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PaC Model in Action
• In the beginning,
SEXP
=Pi∑
1+S,expected payoffs from strangers
Randomly pick
,ini pmC C
a0 a1
Pi is the payoffs achieved each time
is the total number of times talking to a strangerS
See details in the paper
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
4
5$a1
a2
a3
510$
2$EXPS 5$capital
a0
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
4
5$a1
a2
a3
510$
2$EXPS 5$capital
a0
2 5 from a1EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
ask
ask
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
nothing
a3
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$EXPS 4$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
2 5 1. from a2EXPS
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
ask
payoffs = 5$ from a3
2 5 1. from a2EXPS ask
ask
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PaC Model in Action
• Later: call (or not), to max benefit
a1
a2
a3
510$
2 5$.EXPS 2$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
a1
payoffs = 5$ from a3
2 5 1. from a2EXPS nothing
a3
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
2$capital
a0
S EXP 2 5 from 1
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
S EXP 2.5 1 from 2
Randomly pick
a4
Randomly pick a4
S EXP 1.8$
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PaC Model in Action
• Later: call (or not), to max benefit
1
1$
5
7$a1
a2
a3
510$
0$capital
a0
2 5 from a1EXPS
payoffs = 2$ from a1
2 1 from a2EXPS
15$
payoffs = 5$ from a3
2 5 1. from a2EXPS
Randomly pick
a4
Randomly pick a4
10.5$
total payoffs = 2+5+0.5 = 7.5$
payoffs = 0.5$ from a4
S EXP 1.8$
Result: ‘friendly’ agents get many neighbors, formHeavy links, triangles and cliques
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Validation of PaC
• Choose the following parameters– – –
• Ran 35 simulations• 100,000 agents per simulation• Variation of the parameters does not change the
shape of the distribution
0 1 0 4. , .ini pmC C 0 9.
, are uniformly chosen from (0,1)i LF P
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Goals of Validation
? G1: Skewed degree/node weight distribution? G2: Snapshot Power-Law? G3: Skewed connected components distribution? G4: Clique-Degree Power-Law? G5: Clique-Participation Law? G6: Triangle Weight Law
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Validation of PaC
• G1: Skewed Degree / Node Weight Distribution
Real Network
Synthetic Network
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Validation of PaC
• G2: Snapshot Power Law [McGlohon, Akoglu, Faloutsos 08] “more partners, even more calls”
Real Network Synthetic Network
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Validation of PaC
• G3: Skewed distribution of the connected components
Real Network Synthetic Network
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Validation of PaC
• G4: Clique Degree Power Law
Real Network Synthetic Network
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Validation of PaC
• G5: Clique Participation Law
Real Network Synthetic Network
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Validation of PaC
• G6: Triangle Weight Law
Real Network
Synthetic Network
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Validation of PaC
G1: Skewed degree/node weight distributionG2: Snapshot Power-LawG3: Skewed connected components distributionG4: Clique-Degree Power-LawG5: Clique-Participation LawG6: Triangle Weight Law
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Conclusion
• Find properties that cliques hold in real social networks– Q1.1: How does the number of our social
circles relate to our degree ?• Clique-Degree Power Law
– Q1.2: How do people participate into cliques ?• Clique Participation Law
– Q1.3: What patterns do the edge weights follow in triangles ?• Triangle Weight Law
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Conclusion
• Q2: How can we produce an intuitive emergent graph generator based on human’s natural behaviors without using any randomness ?– PaC Model is utility-driven but can still
generate graphs that follow old and new patterns.
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Related Work
• Graph Generators– ER, Preferential Attachment, Forest Fire, Butterfly
Model, ……see survey [Chakrabarti, Faloutsos 06]• Games of network formation
– Bounded Budget Game [Laoutaris et al. 08]– unBounded Budget Game [Fabrikant et al. 03, Albers
et al. 06, Demaine et al. 07]– Bipartite Exchange Economy [Even-Dar et al. 07]
• Properties of mobile phone-call network– [Nanavati et al. 07, Onnela et al. 07, Seshadri et
al.08]
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Questions
Thanks for your attention!
dunan AT cs.cmu.edu christos AT cs.cmu.edu
wangbai AT bupt.edu.cn Lakoglu AT cs.cmu.edu