CS224W: Analysis of Networks Jure Leskovec, Stanford University

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1 CS224W: Analysis of Networks Jure Leskovec, Stanford University

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

2 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 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 2 Unbalanced Inconsistent with the friend of a friend or enemy of the enemy intuition

3 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 3 So far we talked about complete graphs 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 definitions are equivalent!

4 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 If we find a component of nodes on edges that contains a edge Þ Unbalanced 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 Even length cycle 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 4 Odd length cycle

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10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, http://cs224w.stanford.

8 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 8 Using BFS assign each node a side Graph is unbalanced if any two connected supernodes are assigned the same side L R R L û L L Unbalanced! R

10 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 10 Each link AB is explicitly tagged with a sign: Epinions: Trust/Distrust Does A trust B s product reviews? (only positive links are visible to users) 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? Balanced Unbalanced Compare frequencies of signed triads in real and shuffled signs Triad Epinions Wikipedia Consistent with Balance?

11 [CHI 10] Does structural balance hold? Balanced Unbalanced Compare frequencies of signed triads in real and shuffled signs Triad Epinions Wikipedia Consistent with Balance? P(T) P 0 (T) P(T) P 0 (T) ü ü ü û P(T) fraction of a triads P 0 (T) triad fraction if the signs would appear at random Real data Shuffled data 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 11 x x x x x x x

[CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, http://cs224w.stanford.

12 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 12 New setting: Links are directed, created over time Node A links to B Directions and signs of links from/to X provide context A How many r are now explained by balance? Only half (8 out of 16) X B Edge sign according to the balance theory. Do people close triad X with the balanced edge? A B ü X ü ü û û ü ü û ü ü û û û û ü 16 signed directed triads û (in directed networks people traditionally applied balance by ignoring edge directions)

13 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 13 Status in a network [DavisLeinhardt 68] A B :: B has higher status than A A B :: B has lower status than A Note: Here the notion of status is now implicit and governed by the network (rather than using the number of edits of a user as a proxy for status as we did before) Apply status principle transitively over paths Can replace each A B with A B Obtain an allpositive network with same status interpretation

14 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 14 B?? A X?????? Status does not make predictions for all the triads (denoted by?)

15 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 15 X X A B A B Balance: Status: Balance: Status: Status and balance give different predictions!

16 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 16 At a global level (in the ideal case): Status Hierarchy Allpositive directed network should be approximately acyclic Balance Coalitions Balance ignores directions and implies that subgraph of negative edges should be approximately bipartite 3 2 1

17 [CHI 10] Edges are directed: X has links to A and B Now, A links to B (triad ABX) How does sign of A B depend signs from/to X? P(A B X) vs. P(A B) We need to formalize: 1) Links are embedded in triads: Triads provide context for signs 2) Users are heterogeneous in their linking behavior 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 17 A A X? Vs. B B

18 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, [CHI 10] 18 Link A B appears in context X: A B X 16 possible contexts: Note: Context of a red link is uniquely determined by the directions and signs of links from/to X

19 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 19 Users differ in frac. of links they give/receive For a user U: Generative baseline: Frac. of given by U Receptive baseline: Frac. of received by U Basic question: How do different link contexts cause users to deviate from their baselines? Link contexts as modifiers on a person s predicted behavior Def: Surprise: How much behavior of A/B deviates from his/her baseline when A/B is in context X

20 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 20 Intuition: How much behavior of user A in context X deviates from his/her baseline behavior Baseline: For every user A : p g (A i ) generative baseline of A i Fraction of times A i gives a plus Context: (A 1, B 1 X 1 ),, (A n, B n X n ) all instances of triads in context X (A i, B i, X i ) an instance where when user A i links to user B i the triad of type X is created. Say k of those triads closed with a plus k out of n times: A i B i Context X: A A X Vs. B B

21 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 21 Surprise: How much behavior of user A in context X deviates from his/her baseline behavior Generative surprise of context X: s g ( X ) = n å i= 1 k p g å i= 1 ( A )(1 p g (A i ) generative baseline of A i Context X: (A 1, B 1 X 1 ),, (A n, B n X n ) k of instances of triad X closed with a plus edges n i p g ( A ) p Receptive surprise is similar, just use p r (A i ) i g ( A )) i Context X: A A X Vs. B B

Surprise: How much behavior of user deviates from baseline when in context X Generative surprise of context X= 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, http://cs224w.stanford.

22 Surprise: How much behavior of user deviates from baseline when in context X Generative surprise of context X= 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 22 [CHI 10] å å = = = n i i g i g n i i g g A p A p A p k X s 1 1 )) ( )(1 ( ) ( ) ( z y v w q u _ B X A We have 3 triads of context X: (z,u,v), (y,v,w), (q,v,w) They all close with a plus: So k=3 P g (u)=1/2=0.5 P g (v)=2/2=1 S g (X)=(32.5)/ (0.5*0.51*01*0) = 1

23 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 23 Assume status theory is at work What sign does status predict for edge A B? We have to look at this separately from the viewpoint of A and from the viewpoint of B X X A B A B Gen. surprise of A: Rec. surprise of B: Gen. surprise of A: Rec. surprise of B:

24 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 24 X positively endorses A and B Now A links to B X A puzzle: In our data we observe: Fraction of positive links deviates Above generative baseline of A: S g (X) >0 Below receptive baseline of B: S r (X) < 0 Why? A? B

25 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 25 A s viewpoint: Since B has a positive evaluation, B is likely of high status X Thus, evaluation A gives is more likely to be positive than A s baseline behavior A? B

26 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 26 B s viewpoint: Since A has positive evaluation, A is likely to be high status Thus, evaluation B receives A is less likely to be positive than the baseline evaluation B usually receives X? B Surprise of AB deviates in different directions depending on the viewpoint!

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

27 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 27 Determine node status: Assign X status 0 Based on signs and directions of edges set status of A and B A B 1 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

28 [CHI 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 28 Predictions by status and balance: S g (t i ) S r (t i ) B g B r S g S r Mistakes: t 3 t 15 t 2 t 14 t 16

[WWW 10] Edge sign prediction problem Given a network and signs on all but one edge, predict the missing sign Friend recommendation: Predicting whether you know someone vs.

29 [WWW 10] Edge sign prediction problem Given a network and signs on all but one edge, predict the missing sign Friend recommendation: Predicting whether you know someone vs. Predicting what you think of them Setting: Given edge (A,B), predict its sign: Let s look at signed triads (A,B) belongs to: 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 29 A u? v B

30 [WWW 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 30 For the edge (A,B) we examine Its network context: In what types of triads does our rededge participate in? A B Each triad then votes and we determine the sign

31 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 31 Triad

32 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 32 Triad

33 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 33 Triad

34 [WWW 10] 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 34 Prediction accuracy: Observations: Balance Status Triads Epinions 80% 82% 93.5% Slashdot 84% 72% 94.4% Wikipedia 64% 70% 81% Signs can be modeled from local network structure alone! Status works better on Epinions and Wikipedia Wikipedia is harder to model: Votes are publicly visible, which means voters might be applying other mechanisms beyond status

10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, http://cs224w.stanford.edu 35 Do people use these very different linking systems by obeying the same principles?

35 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 35 Do people use these very different linking systems by obeying the same principles? How generalizable are the results across the datasets? Train on row, test on column Train on row dataset, predict on column Nearly perfect generalization of the models even though networks come from very different applications!

36 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 36 Signed networks provide insight into how social computing systems are used: Status vs. Balance More evidence that networks are organized based on status Sign of relationship can be reliably predicted from the local network context ~90% accuracy sign of the edge People use signed edges consistently regardless of particular application Near perfect generalization of models across datasets

37 CS224W: Analysis of Networks Jure Leskovec, Stanford University T

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41 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 41 Positively Evaluated? Negatively Evaluated?

42 Do users improve? Operant conditioning predicts that feedback would guide authors towards better behavior (i.e. upvotes are reward stimuli, and downvotes are punishment stimuli). Skinner, B. F. (1938). The behavior of organisms: An experimental analysis.

43 Or do they get worse? Feedback can have negative effects. People given only positive feedback tend to become complacent. Also, bad impressions are quicker to form and more resistant to disconfirmation. Brinko, K. T. (1993). The practice of giving feedback to improve teaching: what is effective? Baumeister, R. F., Bratslavsky, E., Finkenauer, C., & Vohs, K. D. (2001). Bad is stronger than good.

44 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 44 Evaluations can affect Post quality (How well you write) Community bias (How people perceive you) Posting frequency (How regularly you post) Voting behavior (How you vote on others)

45 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 45 Four large commentbased news communities with 1.2M articles, 1.8M registered users, 42M posts, 140M votes, 1 year CNN IGN Breitbart allkpop

46 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 46 How do we measure community feedback? Number of upvotes Upvotes minus Downvotes Fraction of upvotes

# of downvotes 20 10 0 10 20 # of upvotes 7 =

92 10/12/17 Jure Leskovec, Stanford CS224W:

edu Crowdsourcing exercise: On a scale 17 how

47 # of downvotes # of upvotes 7 = Positive 1 = Negative Fraction of upvotes: R 2 = /12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, Crowdsourcing exercise: On a scale 17 how would you feel about getting X positive and Y negative votes? 47

10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, http://cs224w.

48 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 48 What happens after you give a user a positive, or a negative evaluation?

49 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 49 Compare similar pairs of users who were evaluated differently on similar content 3 posts before 3 posts after Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects.

50 10/12/17 Text quality determined by training a machine learning model using text features, validated using crowd workers. Jure Leskovec, Stanford CS224W: Analysis of Networks, 50 Matching pairs of users

51 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 51 Evaluations can affect Post quality (How well you write) Community bias (How people perceive you) Posting frequency (How regularly you post) Voting behavior (How you vote on others)

52 To learn more about these types of effects, see Kanouse, D. E., & Hanson Jr, L. R. (1987). Negativity in evaluations. 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 52 How much of a future evaluation can be explained by textual effects?

53 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 53 Evaluations can affect Community bias (How people perceive you) How does community perception of a user change after an evaluation?

54 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 54 Upvotes Downvotes Text Quality Community Bias? Actual Evaluation P/(PN) Judged Text Quality Community Bias = 0.1

55 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 55

56 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 56 Positive Eval. More Positive Similar History Similar Text Quality Worse Text Worse Perception Before Negative Eval. After

57 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 57 Evaluations can affect Posting frequency (How regularly you post) Does feedback regulate post quantity?

58 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 58

59 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 59 Evaluations can affect Voting Behavior (How you vote on others) Does feedback result in subsequent backlash?

60 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 60 Proportion of upvotes given Before * After Positive Negative

10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, http://cs224w.stanford.edu 61 Negativelyevaluated users write worse (and more!

61 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 61 Negativelyevaluated users write worse (and more!), are themselves evaluated worse by the community, and evaluate other community members worse. Positivelyevaluated users, on the other hand, don t do any better.

62 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 62

63 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 63 Proportion of downvotes m downvotes 1.7m downvotes 0.16 Jan Feb Mar Apr May Jun Jul Aug

64 10/12/17 Jure Leskovec, Stanford CS224W: Analysis of Networks, 64 CNN 0.23 IGN Jan Mar May Jul 0.10 Jan Mar May Jul Breitbart 0.12 allkpop Jan Mar May Jul 0.05 Nov Jan Mar May

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

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