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arXiv · 0804.0867

Clique percolation

Bela Bollobas·Oliver Riordan
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Abstract

Derenyi, Palla and Vicsek introduced the following dependent percolation model, in the context of finding communities in networks. Starting with a random graph $G$ generated by some rule, form an auxiliary graph $G'$ whose vertices are the $k$-cliques of $G$, in which two vertices are joined if the corresponding cliques share $k-1$ vertices. They considered in particular the case where $G=G(n,p)$, and found heuristically the threshold for a giant component to appear in $G'$. Here we give a rigorous proof of this result, as well as many extensions. The model turns out to be very interesting due to the essential global dependence present in $G'$.

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Bela Bollobas, Oliver Riordan. 2008-04-05. Clique percolation. https://doi.org/10.1002/rsa.20270

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