18-signed_annot

18-signed_annot - CS224W:SocialandInformationNetworkAnalysis

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CS224W: Social and Information Network Analysis re eskovec tanford University Jure Leskovec, Stanford University http://cs224w.stanford.edu
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etworks with ositive nd egative Networks with positive and negative relationships Consider an undirected complete graph Label each edge as either: Positive: friendship, trust, positive sentiment, … egative: nemy, distrust, negative sentiment, … Negative: enemy, distrust, negative sentiment, … Examine triples of connected nodes A,B, C 11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
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Consider edges as undirected Start with intuition [Heider ’46] : Friend of my friend is my friend nemy f nemy my iend Enemy of enemy is my friend Enemy of friend is my enemy Look at connected triples of nodes: + + + + + + nbalanced alanced Unbalanced Balanced Consistent with “friend of a friend” or “enemy of the enemy” intuition Inconsistent with the “friend of a friend” or “enemy of the enemy” intuition Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 11/17/2010 3
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raph is alanced every connected triple of Graph is balanced if every connected triple of nodes has all 3 edges labeled +, or else exactly edge is labeled + 1 edge is labeled +. 11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 4 Balanced Unbalanced
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alance implies global coalitions artwright arary Balance implies global coalitions [Cartwright Harary] If all triangles are balanced, then either: he network contains only positive edges or The network contains only positive edges, or Nodes can be split into 2 factions linked by negative edges X Y + + + 11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 5
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Every node in X is enemy ofY B D + Every 2 nodes X are friends Every 2 nodes InY are friends A + In X are friends C E 11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 6 Friends of A Enemies of A
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ternational relations: International relations: Positive edge: alliance egative dge: animosity Negative edge: animosity Separation of Bangladesh from Pakistan in 1971: U S supports P akistan. Why? USS R was enemy of C hina C hina was enemy of I ndia P I I ndia was enemy of P akistan U S was friendly with C hina C C hina vetoed Bangladesh 11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 7 R U
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11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 8
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11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 9
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11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 10
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11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 11
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11/17/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 12
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This note was uploaded on 01/11/2011 for the course CS 224 at Stanford.

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18-signed_annot - CS224W:SocialandInformationNetworkAnalysis

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