Clique percolation

Béla Bollobás, Oliver Riordan
2009 Random structures & algorithms (Print)  
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
more » ... his result, as well as many extensions. The model turns out to be very interesting due to the essential global dependence present in G'.
doi:10.1002/rsa.20270 fatcat:5jm7njovmjeulhrees2a7kffdm