Social Network Analysis

1. Social Network Analysis BY Hani Maher Ahmad

2. What is Social Network • Social Network is heterogynous and multirelational data set represented by graph • Social networks need not to be social in context • Examples : • Electrical power grids • The web • Coauthorship

3. Why do we study Social Network • Small world effect & universal behavior • 100th Monkey effect & tipping behavior • It is a complex Dynamical System • More information in Data Mining • Links information and structure of data are involved in the mining process • More realistic applications • New types of patterns (e.g. link prediction)

4. What do you thinkSmall world Experiment • People in city X are asked to direct message to stranger in city Y • By forwarding it to friend they think he know the stranger • What is the number of intermediate peoples links until message is received?

5. Small World • It is a graph have high degree of local clustering • Six degree of separation E.g. Science Coauthorship Graph

6. Small World

7. What Do you think100th monkey effect

8. What do you think • Why there are a sudden events in our life? • How dose on product or movie or idea spread at once ? • Why do the most smart students became smart suddenly ? • Why dose we change our mind suddenly?

9. Evolution of a Random Network • We have a large number n of vertices • We start randomly adding edges one at a time • At what time t will the network: • have at least one “large” connected component? • have a single connected component? • have “small” diameter?

10. crime rate size of police force Formalizing Familiar Ideas • Explaining universal behavior through statistical models • our models will always generate many networks • almost all of them will share certain properties (universals) • Explaining tipping through incremental growth • we gradually add edges • many properties will emerge very suddenly during this process prob. NW connected number of edges

11. How to study SN • Random graph generation models E.g. Forest Fire model 1. chooses an ambassador node w. 2. selects x links incident to w randomly . Let w1;w2; …;wx denote the nodes at the other end of the selected edges. 3. Our new node, v, forms out-links to w1;w2; …;wx and then applies step 2 recursively to w1;w2;…;wx. The process continues until it dies out

12. How to study SN • The models are realistic and tell how the reality will be • It is seen that rich become richer • But it is blind and cant tell how things happen exactly • Very hard to predict exactly since most of the problems are NP-hard

13. Dynamical System • It is a state and a rule changing that state • E.g. pupation number is a state and logistic growth is a rule

14. Dynamical Systems • Dynamical Systems has important property of attractors (points of stability )

15. Dynamical Systems • But some times a chaotic behavior or divergence occur like when traffic network become stuck • We study social network to control its stability and prevent chaos

16. Social Network Characteristics • Densification power Law • Number of edges grows exponentially with number of nods • Shrinking diameter • The effective diameter of network shrink with network growth • Heavy-tailed out degree and in degree • The number of out and in degree follow the heavy tail distribution

17. What do you think • What are things can be mined from social network? • What is the difference and similarity of data and network mining ? • Dose the graph need to be labeled or not ? • Dose the graph need to be directed or not ? • Can we mine the graph for all and exact patterns?

18. Link Mining tasks • Link based object classification • Category is classified based on links and attributes (generalize data classification) • Object type prediction • Link type prediction • Predicting link existence • Link cardinality estimation

19. Link mining tasks • Object reconciliation • To detect if two objects are the same • E.g. if two desires are the same or two paper sites are the same • Group detection • Sub graph detection What is the difference between 7 and 8 ?

20. Are you looking for her • Who is the most perfect woman ? • In other word how can we find the most valuable object in the network and how can we find the rank of an object ? • How can we find her prestige .

21. Representing Network in suitable way for computation • We can represent the graph with matrices • Adjacency matrix • the rows and columns represent nodes with entries equal 1 if there is an edge and 0 else • Incidence matrix • the rows and columns represent nodes and edges with entries equal 1 if the edge is incident to node and 0 else

22. Adjacency matrix of a network

23. Three algorithms • Prestige algorithm • Page rank • HITS authority and hubs Note : the first two compute the prestige vectored of the network representing the prestige of each node the third algorithm compute the hub score vector and authority score vector

24. Prestige algorithm • The prestige of a node depend on the prestige of nodes pointing to it. • That is for node i : P[i] = AT[i].P • sum of nodes pointing to it * there prestige • For all nodes P = AT.P • Starting from all prestige in the beginning = 1 • Apply the multiplication until converge • i.e. Pt+1 = AT.Pt

25. Page Rank Algorithm • For node prestige dose not depend only on the prestige of nodes pointing to it but also on a randomly chosen nodes • Random surfing model: • At any page, • With prob. , randomly jumping to a page • With prob. (1 – ), randomly picking a link to follow • Page rank = prestige + random walk

26. Page Rank Algorithm • Note that the adjacency matrix is normalized • This is the main algorithm behind google

27. HITS Algorithm • This algorithm give two ranks to the node . • As authority if it has been pointed to by many good hubs • and hub if it point to many good authorities.

28. HITS

29. Application : Viral Marketing • The marketing has many models • Direct marketing : • based on customer attributes • classification problem • Massive marketing : • based on the population segment the person belong to • clustering problem • have advantage that it capture indirect costumers • Viral marketing : • massive marketing + optimize word of mouth effect

30. Application : Viral Marketing • E.g. a person how buy a car motivate his friends to buy a car • Aim is to find Network value of person • If the person is a good hub it is potential customer that can maximize the network profit so spend more money in marketing product to him • If the person have negative effect don’t market to him

31. Application : Viral Marketing • Viral Marketing can be used in non marketing tasks • E.g. • Fighting teenage smoking • Stopping virus spread • Spread an idea • marketing for a Political men “e.g. election”

32. So What do you think • She has the best authority score all “hubs” are pointing to her. • Is it a good idea to marry her ?? Yes or NO

33. What do you think • She can have best authority because of • Rich become richer • Some tipping phenomena • She is modda • She have more hubs • Because of butterfly effect and divergence • She can appear due to marketing effort • She also can be good authority

34. So What do you think • Google use the page rank and HITS do you think that the result are perfect or just popular • Dose that make sense when working with real people in the real world • So for me it is Big NO

35. Social Networks out of control • If the social network is not controlled • Rich will become richer and all the capital will accumulate with him • Most people like the wrong things due to joy of adrenaline and self prodding • Many stuck in the relation ships will occur as bas ideas , drugs , bad practices spreading • Many silly persons will appear as authority due to there strange or bad ideas

36. Social Networks out of control • The number of links will become Extremely large making life harder and noisy and much loose in time • The diameter will shrink making the spy and crimes easy • Some tipping events will destroy the society • More effort will be on marketing instead of industry • The civilization will stop and we only will focus on communication

37. Social Networks out of control • Hidden persons can control the network and affection others by making adjusting links and spreading ideas “program the SN” to there benefits • It is not proved but I guess a sudden death of the network will occur . “ we are running into Chaos”

38. What is the solution ??

39. References • The text book • The another slides • Dr Mohammed Zaki lectures “one of the leading data mining researcher” • http://www.cs.rpi.edu/~zaki/www-new/pmwiki.php/Dmcourse/Main • SATNAM ALAG : Collective Intelligence in Action • Wikipedia : small worlds , social networks articles • Kathleen T. Alligood : CHAOS An Introduction to Dynamical Systems

40. Thank you Questions ???