Large Human Communication Networks Patterns and a Utility-Driven Generator

1. 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

2. Human Communication Network

3. 0 2 4 1 3 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.

4. 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 ?

5. Outline • Motivation • Q1: Observations • Q2: Utility-Driven Model • Conclusion • Related Work

6. 3 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> Multiple interactions are represented as edge weight.

7. Observation 1 Question 1.1 : How does the number of our social circles (maximal cliques) relate to our degree

8. Observation 1 Clique-Degree Power-Law More friends, even more social circles !

9. Observation 1 Clique-Degree Power-Law • Outlier Detection Spammer-like!

10. Observation 2 Question 1.2 : What is the distribution of clique participation ?

11. Observation 2 Clique-Participation Law

12. Observation 3 Question1.3 : Nodes in a triangle are topologically equivalent. Will they also give equal number of phone calls to each other ? Max Weight Min Weight Mid Weight

13. Observation 3 Triangle Weight Law

14. Outline • Motivation • Q1: Observations • Q2: Utility-Driven Model • Conclusion • Related Work

15. 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

16. 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

17. agent PaC Model • People can benefit from calling each other. • A Pay and Call game = PaC Model • The payoffs are measured as “emotional dollars”.

18. 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 Outline of Agent Behavior Exponential lifetime Rich get richer Closing Triangle

19. 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)

20. PaC Model - formulas

21. Randomly pick a0 a1 PaC Model in Action • In the beginning, See details in the paper

22. PaC Model in Action • Later: call (or not), to max benefit 4 a1 5$ 1 10$ 5 1$ a2 a0 a3

23. PaC Model in Action • Later: call (or not), to max benefit 4 a1 5$ 1 10$ 5 1$ a2 a0 a3

24. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 5 a1 7$ 1 10$ 5 1$ a2 a0 a3

25. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 5 a1 7$ 1 10$ 5 1$ a2 a0 a3

26. ask PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 ask a1 10$ 5 a2 a0 a3

27. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 a3 a1 nothing 10$ 5 a2 a0 a3

28. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 5 a1 7$ 1 10$ 5 1$ a2 a0 a3

29. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 payoffs = 5$ from a3 5 a1 7$ 1 10$ 5 1$ 1 a2 a0 5$ a3

30. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 payoffs = 5$ from a3 5 a1 7$ 1 10$ 5 1$ 1 a2 a0 5$ a3

31. ask PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 payoffs = 5$ from a3 ask a1 10$ 5 ask a2 a0 a3

32. PaC Model in Action • Later: call (or not), to max benefit payoffs = 2$ from a1 payoffs = 5$ from a3 a3 a1 nothing 10$ 5 a1 a2 a0 a3

33. PaC Model in Action • Later: call (or not), to max benefit Randomly pick payoffs = 2$ from a1 a4 payoffs = 5$ from a3 5 a1 7$ 1 10$ 5 Randomly pick a4 1$ 1 a2 a0 5$ a3

34. PaC Model in Action • Later: call (or not), to max benefit Randomly pick payoffs = 2$ from a1 a4 1 payoffs = 5$ from a3 0.5$ 5 a1 7$ 1 10$ 5 Randomly pick a4 1$ 1 a2 payoffs = 0.5$ from a4 a0 5$ total payoffs = 2+5+0.5 = 7.5$ a3 Result: ‘friendly’ agents get many neighbors, form Heavy links, triangles and cliques

35. 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

36. 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

37. Validation of PaC • G1: Skewed Degree / Node Weight Distribution Real Network Synthetic Network

38. Validation of PaC • G2: Snapshot Power Law [McGlohon, Akoglu, Faloutsos 08] “more partners, even more calls” Real Network Synthetic Network

39. Validation of PaC • G3: Skewed distribution of the connected components Real Network Synthetic Network

40. Validation of PaC • G4: Clique Degree Power Law Real Network Synthetic Network

41. Validation of PaC • G5: Clique Participation Law Real Network Synthetic Network

42. Validation of PaC • G6: Triangle Weight Law Real Network Synthetic Network

43. Validation of PaC • 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

44. 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

45. Conclusion • Q2: How can we produce an intuitive emergent graph generator based on human’s natural behaviors without using any randomness ? • PaC Modelis utility-driven but can still generate graphs that follow old and new patterns.

46. 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]

47. 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