CS224W: Social and Information Network Analysis Jure Leskovec, Stanford University

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1 CS224W: Social and Information Network Analysis Jure Leskovec, Stanford University

2 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 2 Networks with positive and negative relationships Consider an undirected complete graph Label each edge as either: Positive: friendship, trust, positive sentiment, Negative: enemy, distrust, negative sentiment, Examine triples of connected nodes A, B, C

3 Start with the intuition [Heider 46]: Friend of my friend is my friend Enemy of enemy is my friend Enemy of friend is my enemy Look at connected triples of nodes: Balanced Consistent with friend of a friend or enemy of the enemy intuition 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 3 Unbalanced Inconsistent with the friend of a friend or enemy of the enemy intuition

4 Graph is balanced if every connected triple of nodes has: all 3 edges labeled, or exactly 1 edge labeled Unbalanced Balanced 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 4

5 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 5 Balance implies global coalitions [CartwrightHarary] If all triangles are balanced, then either: The network contains only positive edges, or Nodes can be split into 2 sets where negative edges only point between the sets L R

6 B Every node in L is enemy of R D Any 2 nodes in L are friends A Any 2 nodes in R are friends C L Friends of A Enemies of A 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 6 E R

7 International relations: Positive edge: alliance Negative edge: animosity Separation of Bangladesh from Pakistan in 1971: US supports Pakistan. Why? USSR was enemy of China China was enemy of India India was enemy of Pakistan US was friendly with China China vetoed Bangladesh from U.N.? 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 7 P U B? C I R

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10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 14 Balanced?

14 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 14 Balanced? Def 1: Local view Fill in the missing edges to achieve balance Def 2: Global view Divide the graph into two coalitions The 2 defs. are equivalent!

15 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 15 Graph is balanced if and only if it contains no cycle with an odd number of negative edges. How to compute this? Find connected components on edges For each component create a supernode Connect components A and B if there is a negative edge between the members Assign supernodes to sides using BFS

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10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.

19 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 19 Using BFS assign each node a side Graph is unbalanced if any two supernodes are assigned the same side L R R L L L Unbalanced! R

[CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.

20 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 20 Each link A B is explicitly tagged with a sign: Epinions: Trust/Distrust Does A trust B s product reviews? (only positive links are visible) Wikipedia: Support/Oppose Does A support B to become Wikipedia administrator? Slashdot: Friend/Foe Does A like B s comments? Other examples: Online multiplayer games

[CHI 10] Does structural balance hold? Triad Epinions Wikipedia P(T) P 0 (T) P(T) P 0 (T) Balance 0.87 0.62 0.70 0.49 0.07 0.05 0.21 0.10 0.05 0.32 0.08 0.49 0.007 0.003 0.011 0.

21 [CHI 10] Does structural balance hold? Triad Epinions Wikipedia P(T) P 0 (T) P(T) P 0 (T) Balance P(T) probability of a triad P 0 (T) triad probability if the signs would be random Real data Shuffled data 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 21 x x x x x x x

22 22 Intuitive picture of social network in terms of densely linked clusters How does structure interact with links? Embeddedness of link (A,B): Number of shared neighbors

23 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 23 Embeddedness of ties: Positive ties tend to be more embedded Positive ties tend to be more clumped together Public display of signs (votes) in Wikipedia further attenuates this Epinions Wikipedia

24 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, [CHI 10] 24 Clustering: net: More clustering than baseline net: Less clustering than baseline Size of connected component: /net: Smaller than the baseline

25 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 25 New setting: Links are directed and created over time X A B How many are now explained by balance? Only half (8 out of 16) Is there a better explanation? Yes. Status. 16 *2 signed directed triads

26 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 26 Links are directed and created over time Status theory [DavisLeinhardt 68, Guha et al. 04, Leskovec et al. 10] Link A B means: B has higher status than A Link A B means: B has lower status than A Status and balance give different predictions: X X A B A B Balance: Status: Balance: Status:

27 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 27 Edges are directed Edges are created over time X has links to A and B Now, A links to B (triad ABX) How does sign of AB depend signs of X? We need to formalize: Links are embedded in triads: Provides context for signs Users are heterogeneous in their linking behavior A A X? X B B

28 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, [CHI 10] 28 Link (A,B) appears in the context (A,B; X) 16 different contextualized links:

29 [CHI 10] Surprise: How much behavior of user deviates from baseline in context t: (A 1, B 1 ; X 1 ),, (A n, B n ; X n ) instances of contextualized link t k of them closed with a plus p g (A i ) generative baseline of A i empirical prob. of A i giving a plus Then: generative surprise of n triad type t: k pg ( Ai ) s i= 1 g ( t) = n i p g ( A )(1 p i g ( A )) 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 29 i A A X Vs. X B B

30 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 30 Two basic examples: X X A B A B Gen. surprise of A: Rec. surprise of B: Gen. surprise of A: Rec. surprise of B:

statusconsistent, if: Gen. surprise is statusconsistent if it has same sign as status of B Rec.

31 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 35 Determine node status: Assign X status 0 Based on signs and directions of edges set status of A and B 1 A B Surprise is statusconsistent, if: Gen. surprise is statusconsistent if it has same sign as status of B Rec. surprise is statusconsistent if it has the opposite sign from the status of A Surprise is balanceconsistent, if: If it completes a balanced triad 1 X 0 Statusconsistent if: Gen. surprise > 0 Rec. surprise < 0

32 [CHI 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 36 Predictions: S g (t i ) S r (t i ) B g B r S g S r t 3 t 15 t 2 t 14 t 16

edu 37 Both theories make predictions about the global structure of the network Structural

33 [WWW 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 37 Both theories make predictions about the global structure of the network Structural balance Factions Find coalitions Status theory Global Status Flip direction and sign of minus edges Assign each node a unique status so that edges point from low to high 3 1 2

34 [WWW 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 38 Fraction of edges of the network that satisfy Balance and Status? Observations: No evidence for global balance beyond the random baselines Real data is 80% consistent vs. 80% consistency under random baseline Evidence for global status beyond the random baselines Real data is 80% consistent, but 50% consistency under random baseline

35 [WWW 10] Edge sign prediction problem Given a network and signs on all but one edge, predict the missing sign Machine Learning Formulation: Predict sign of edge (u,v) Class label: Dataset: 1: positive edge 1: negative edge Learning method: Logistic regression u Original: 80% edges Balanced: 50% edges Evaluation: Accuracy and ROC curves Features for learning: Next slide? v 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 39

36 [WWW 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 40 For each edge (u,v) create features: Triad counts (16): Counts of signed triads u edge u v takes part in Node degree (7 features): Signed degree: d out(u), d out(u), d in(v), d in(v) Total degree: d out (u), d in (v) Embeddedness of edge (u,v) v

[WWW 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 41 Classification Accuracy: Epinions: 93.5% Slashdot: 94.

37 [WWW 10] 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 41 Classification Accuracy: Epinions: 93.5% Slashdot: 94.4% Wikipedia: 81% Signs can be modeled from local network structure alone Trust propagation model of [Guha et al. 04] has 14% error on Epinions Triad features perform less well for less embedded edges Wikipedia is harder to model: Votes are publicly visible Epin Slash Wiki

38 42

10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 43 Do people use these very different linking systems by obeying the same principles?

39 10/10/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, 43 Do people use these very different linking systems by obeying the same principles? How generalizable are the results across the datasets? Train on row dataset, predict on column Nearly perfect generalization of the models even though networks come from very different applications

40 44 Signed networks provide insight into how social computing systems are used: Status vs. Balance Different role of reciprocated links Role of embeddedness and public display Sign of relationship can be reliably predicted from the local network context ~90% accuracy sign of the edge

41 Status difference (AB) More evidence that networks are globally organized based on status People use signed edges consistently regardless of particular application Near perfect generalization of models across datasets Many further directions: Status difference of nodes A and B [ICWSM 10]: A<B A=B A>B

CS224W: Analysis of Networks Jure Leskovec, Stanford University

CS224W: Analysis of Networks Jure Leskovec, Stanford University http://cs224w.stanford.edu Start with the intuition [Heider 46]: Friend of my friend is my friend Enemy of enemy is my friend Enemy of friend