Number of cliques in random scale-free network ensembles
Statistical Mechanics
2009-11-11 v1 Physics and Society
Abstract
In this paper we calculate the average number of cliques in random scale-free networks. We consider first the hidden variable ensemble and subsequently the Molloy Reed ensemble. In both cases we find that cliques, i.e. fully connected subgraphs, appear also when the average degree is finite. This is in contrast to what happens in Erd\"os and Renyi graphs in which diverging average degree is required to observe cliques of size . Moreover we show that in random scale-free networks the clique number, i.e. the size of the largest clique present in the network diverges with the system size.
Keywords
Cite
@article{arxiv.cond-mat/0606088,
title = {Number of cliques in random scale-free network ensembles},
author = {Ginestra Bianconi and Matteo Marsili},
journal= {arXiv preprint arXiv:cond-mat/0606088},
year = {2009}
}
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(15 pages)