Termination of Multipartite Graph Series Arising from Complex Network Modelling

An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs. However, this approach has, until now, severe limitations resulting from its incapacity to reproduce a key property of this object: the overlapping nature of cliques in complex networks. In order to get rid of these limitations we propose to encode the structure of clique overlaps in a network thanks to a process consisting in iteratively factorising the maximal bicliques between the upper level and the other levels of a multipartite graph. We show that the most natural definition of this factorising process leads to infinite series for some instances. Our main result is to design a restriction of this process that terminates for any arbitrary graph. Moreover, we show that the resulting multipartite graph has remarkable combinatorial properties and is...

• Type: Journal
• Year: 2010
• Where: COCOA
• Authors: Matthieu Latapy, Thi Ha Duong Phan, Christophe Crespelle, Thanh Qui Nguyen
• Keywords: Clique, COCOA 2010, Complex Network, Discrete Geometry, Multipartite Graph