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Understanding Bipartite Networks: Biological, Cognitive, and Cultural Connections

This document explores the concept of bipartite networks (BNWs) through various combinatorial systems, including biological genes, linguistic words, and cocktails. It provides insights into the structural properties of BNWs, their degree distributions, centrality measures, and clustering coefficients. Additionally, it discusses the significance of bipartite graphs in different real-world applications such as movies, authors, and metabolic pathways. Analyzing these networks reveals the intricate relationships that bind different entities across various domains, shedding light on their unifying characteristics.

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Understanding Bipartite Networks: Biological, Cognitive, and Cultural Connections

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  1. Bipartite Networks - I Monojit Choudhury Microsoft Research India

  2. Evolution: Biological, Cognitive and Cultural Words Genes Cocktails

  3. What’s 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

  4. A Model of DCS AAU ACG ACC AAU UGC AUA AAU GAA UGA ACG … … AAU V: genes UGA ACC UGC AUA … … GAA U: codons AGA … ACG

  5. More Examples Letters Words Sentences c cat likes rat n cat a rat likes cat t likes r cat eats rat l rat rat eats cat i k the cat likes rat eats e cat eats the rat s h the the cat likes the rat z

  6. A Bipartite World • Movie-Actor • Article-Author • Team-Player • Board-Director • Train-Station • Metabolic pathway-Protein • Antibody-Antigen • Language-Phoneme, …

  7. Secrets of Bollywood • How many actors does a movie have and why? • How many movies an actor acts in and why?

  8. BNWs: What’s so Special? • BNW  2-colorability  Triangle free • Aka Two-mode graphs • Generalization: k-partite graphs • k = 1: unipartite (nothing special) • k = 2: BNW • k > 2: not very interesting • Relationship between chromatic number and k

  9. Analysis of BNWs: Degree • Degree distribution • Two separate distributions: one for each partition • Degree Centrality • Do we need any modification? • Yes! Need different normalizations

  10. Analysis of BNW: Centrality • What about • Closeness centrality? • Betweenness centrality • Eigenvector centrality • M. Everett and S.P. Borgatti (2005) Extending Centrality. In Models and Methods in Social Network Analysis. Ed. Carrington et al. CUP

  11. 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.

  12. /s/ One-mode Projection /s/ l2 1 1 l1 /p/ 1 1 1 /k/ /n/ 3 l2 /k/ 2 l3 l1 1 1 2 1 1 l3 One-mode projection /t/ One-mode projection 1 2 1 2 /t/ /d/ l4 l4 1 /d/ 2 1 /p/ /n/ PlaNet LangGraph PhoNet B′ B l1l2l3l4 A l1l2l3l4 /s/ /p/ /k/ /t/ /d/ /n/ l1 l2 l3 l4 0 1 1 1 1 0 1 3 1 1 0 2 1 0 1 0 0 0 0 1 1 1 0 0 /s/ /p/ /k/ /t/ /d/ /n/ 1 3 2 0 /s/ /p/ /k/ /t/ /d/ /n/ 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 2 2 1 1 1 2 0 2 1 1 0 2 2 0 1 2 0 1 1 1 0 1 1 1 1 2 1 0 ATA – D′ AAT – D

  13. Bipartite Structure of all Complex Networks • Jean-Loup Guillaume, Matthieu Latapy (2004) Bipartite structure of all complex networks. Information Processing Letters 90

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