1. Du, Faloutsos, Wang, Akoglu Large Human Communication Networks Patterns and a Utility-Driven Generator Nan Du 1,2, Christos Faloutsos 2, Bai Wang 1, Leman Akoglu 2 1 Beijing University of Posts and Telecommunications, 2 Carnegie Mellon University

2. Du, Faloutsos, Wang, Akoglu 2 Human Communication Network

3. Du, Faloutsos, Wang, Akoglu 3 Clique Real social networks have many triangles. What about the cliques ? Clique is a complete subgraph, which describes a group of closely related friends. If a clique can not be contained by any larger clique, 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. 20 13 4

4. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 5 Outline Motivation Q1: Observations Q2: Utility-Driven Model Conclusion Related Work

6. Du, Faloutsos, Wang, Akoglu 6 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 3 Multiple interactions are represented as edge weight.

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

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

9. Du, Faloutsos, Wang, Akoglu 9 Observation 1 Clique-Degree Power-Law Outlier Detection Spammer-like!

10. Du, Faloutsos, Wang, Akoglu 10 Observation 2 Question 1.2 : What is the distribution of clique participation ?

11. Du, Faloutsos, Wang, Akoglu 11 Observation 2 Clique-Participation Law

12. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 13 Observation 3 Triangle Weight Law

14. Du, Faloutsos, Wang, Akoglu 14 Outline Motivation Q1: Observations Q2: Utility-Driven Model Conclusion Related Work

15. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 17 PaC Model People can benefit from calling each other. A Pay and Call game = PaC Model The payoffs are measured as “emotional dollars”. agent

18. Du, Faloutsos, Wang, Akoglu 18 Outline of Agent Behavior Step 1: decide to stay (P L ) 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

19. Du, Faloutsos, Wang, Akoglu PaC model - details Benefit of a phonecall between agent a i and a j Benefit drops with length of each phonecall (‘saturation’, diminishing returns in economics) Cost of a phonecall between agent a i and a j Start-up cost (C ini ) Cost-per-minute (C pm ) 19

20. Du, Faloutsos, Wang, Akoglu 20 PaC Model - formulas – –

21. Du, Faloutsos, Wang, Akoglu 21 PaC Model in Action In the beginning, Randomly pick a0 a1 See details in the paper

22. Du, Faloutsos, Wang, Akoglu 22 PaC Model in Action Later: call (or not), to max benefit 1 1$ 4 5$ a1 a2 a3 510$ a0

23. Du, Faloutsos, Wang, Akoglu 23 PaC Model in Action Later: call (or not), to max benefit 1 1$ 4 5$ a1 a2 a3 510$ a0

24. Du, Faloutsos, Wang, Akoglu 24 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1

25. Du, Faloutsos, Wang, Akoglu 25 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1

26. Du, Faloutsos, Wang, Akoglu 26 PaC Model in Action Later: call (or not), to max benefit a1 a2 a3 510$ a0 payoffs = 2$ from a1 ask

27. Du, Faloutsos, Wang, Akoglu 27 PaC Model in Action Later: call (or not), to max benefit a1 a2 a3 510$ a0 payoffs = 2$ from a1 nothing a3

28. Du, Faloutsos, Wang, Akoglu 28 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1

29. Du, Faloutsos, Wang, Akoglu 29 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1 1 5$ payoffs = 5$ from a3

30. Du, Faloutsos, Wang, Akoglu 30 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1 1 5$ payoffs = 5$ from a3

31. Du, Faloutsos, Wang, Akoglu 31 PaC Model in Action Later: call (or not), to max benefit a1 a2 a3 510$ a0 payoffs = 2$ from a1 ask payoffs = 5$ from a3 ask

32. Du, Faloutsos, Wang, Akoglu 32 PaC Model in Action Later: call (or not), to max benefit a1 a2 a3 510$ a0 payoffs = 2$ from a1 a1 payoffs = 5$ from a3 nothing a3

33. Du, Faloutsos, Wang, Akoglu 33 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1 1 5$ payoffs = 5$ from a3 Randomly pick a4 Randomly pick a4

34. Du, Faloutsos, Wang, Akoglu 34 PaC Model in Action Later: call (or not), to max benefit 1 1$ 5 7$ a1 a2 a3 510$ a0 payoffs = 2$ from a1 1 5$ payoffs = 5$ from a3 Randomly pick a4 Randomly pick a4 1 0.5$ total payoffs = 2+5+0.5 = 7.5$ payoffs = 0.5$ from a4 Result: ‘friendly’ agents get many neighbors, form Heavy links, triangles and cliques

35. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 37 Validation of PaC G1: Skewed Degree / Node Weight Distribution Real Network Synthetic Network

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

39. Du, Faloutsos, Wang, Akoglu 39 Validation of PaC G3: Skewed distribution of the connected components Real NetworkSynthetic Network

40. Du, Faloutsos, Wang, Akoglu 40 Validation of PaC G4: Clique Degree Power Law Real NetworkSynthetic Network

41. Du, Faloutsos, Wang, Akoglu 41 Validation of PaC G5: Clique Participation Law Real NetworkSynthetic Network

42. Du, Faloutsos, Wang, Akoglu 42 Validation of PaC G6: Triangle Weight Law Real Network Synthetic Network

43. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 45 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.

46. Du, Faloutsos, Wang, Akoglu 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. Du, Faloutsos, Wang, Akoglu 47 Questions Thanks for your attention ！ dunan AT cs.cmu.edu christos AT cs.cmu.edu wangbai AT bupt.edu.cnLakoglu AT cs.cmu.edu