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Termination of Multipartite Graph Series Arising from Complex Network Modelling

Matthieu Latapy 1 Thi Ha Duong Phan 2 Christophe Crespelle 3, 4, 1 Thanh Qui Nguyen 5
1 ComplexNetworks
LIP6 - Laboratoire d'Informatique de Paris 6
3 DNET - Dynamic Networks
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : 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 closely related to another fundamental combinatorial object. Finally, we show that, in practice, this multipartite graph is computationally tractable and has a size that makes it suitable for complex network modelling.
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Contributor : Christophe Crespelle Connect in order to contact the contributor
Submitted on : Wednesday, November 23, 2011 - 7:05:19 PM
Last modification on : Monday, October 11, 2021 - 1:48:01 PM

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Matthieu Latapy, Thi Ha Duong Phan, Christophe Crespelle, Thanh Qui Nguyen. Termination of Multipartite Graph Series Arising from Complex Network Modelling. 4th Annual International Conference on Combinatorial Optimization and Applications - COCOA'10, Dec 2010, Hawaii, Big Island, United States. pp.1-10, ⟨10.1007/978-3-642-17458-2_1⟩. ⟨hal-00644239⟩



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