A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
Bipartite structure of all complex networks
Information Processing Letters
Enumeration aspects of maximal cliques and bicliques
Discrete Applied Mathematics
Towards a bipartite graph modeling of the internet topology
Computer Networks: The International Journal of Computer and Telecommunications Networking
Hi-index | 0.00 |
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.