Large Human Communication Networks Patterns and a Utility-Driven Generator

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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1 3

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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