Bipartite Networks - I Monojit Choudhury Microsoft Research India Evolution: Biological, Cognitive and Cultural Words Genes Cocktails Whats common? Words: Sequences of letters Genes: Sequences of codons Cocktails: Combinations of liquors They are all Combinatorial Systems Discrete Combinatorial System: genes, words Blending System: colors, cocktails A Model of DCS AAU ACG ACC AAU UGC AUA AAU GAA UGA ACG U: codons AAU UGA ACC UGC AUA GAA AGA ACG V: genes More Examples rat likes cat eats the n a t r l i k e s h z c cat likes rat rat likes cat cat eats rat rat eats cat the cat likes rat cat eats the rat the cat likes the rat LettersWords Sentences A Bipartite World Movie-Actor Article-Author Team-Player Board-Director Train-Station Metabolic pathway-Protein Antibody-Antigen Language-Phoneme, Secrets of Bollywood How many actors does a movie have and why? How many movies an actor acts in and why? BNWs: Whats so Special? BNW 2-colorability Triangle free Aka Two-mode graphs Generalization: k-partite graphs o k = 1: unipartite (nothing special) o k = 2: BNW o k > 2: not very interesting Relationship between chromatic number and k Analysis of BNWs: Degree Degree distribution o Two separate distributions: one for each partition Degree Centrality o Do we need any modification? o Yes! Need different normalizations Analysis of BNW: Centrality What about o Closeness centrality? o Betweenness centrality o Eigenvector centrality M. Everett and S.P. Borgatti (2005) Extending Centrality. In Models and Methods in Social Network Analysis. Ed. Carrington et al. CUP Analysis of BNW: Clustering What is the clustering coefficient of a BNW? Basic Idea: Count the squares instead of triangles Zhang et al (2008) The clustering coefficient and community structure of bipartite networks. One-mode Projection One-mode projection l 1 l 2 l 3 l 4 /s/ /p/ /k/ /t/ /d/ /n/ A AA T D /s/ /p/ /k/ /t/ /d/ /n/ B /s/ /p/ /k/ /t/ /d/ /n/ l1l1 l2l2 l3l3 l4l4 /s/ /p/ /k/ /d/ /t/ /n/ PlaNet /s/ /n//k/ /p/ /t//d/ PhoNet l 1 l 2 l 3 l 4 l1l2l3l4l1l2l3l BB l1l1 l2l2 l3l3 l4l LangGraph One-mode projection A T A D Bipartite Structure of all Complex Networks Jean-Loup Guillaume, Matthieu Latapy (2004) Bipartite structure of all complex networks. Information Processing Letters 90