Cliques in rank-1 random graphs: the role of inhomogeneity

Abstract

We study the asymptotic behavior of the clique number in rank-1 inhomogeneous random graphs, where edge probabilities between vertices are roughly proportional to the product of their vertex weights. We show that the clique number is concentrated on at most two consecutive integers, for which we provide an expression. Interestingly, the order of the clique number is primarily determined by the overall edge density, with the inhomogeneity only affecting multiplicative constants or adding at most a $\log \log (n)$ multiplicative factor. For sparse enough graphs the clique number is always bounded and the effect of inhomogeneity completely vanishes.

arXiv comment29 pages

References in corpus (6)

• The phase transition in inhomogeneous random graphs
• Generating simple random graphs with prescribed degree distribution
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• Number of cliques in random scale-free network ensembles
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Cited by in corpus (4)

• Weakly interacting oscillators on dense random graphs
• Cliques in geometric inhomogeneous random graph
• Quasi-cliques in inhomogeneous random graphs
• Large independent sets in recursive Markov random graphs