Emergence of large cliques in random scale-free networks

In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c > 3 are present in random Erdos and Renyi graphs only in the limit of diverging average connectivity. Starting from the finding that real scale-free graphs have large cliques, we study the clique number in uncorrelated scale-free networks finding both upper and lower bounds. Interestingly, we find that in scale-free networks large cliques appear also when the average degree is finite, i.e. even for networks with power law degree distribution exponents gamma is an element of (2, 3). Moreover, as long as gamma< 3, scale-free networks have a maximal clique which diverges with the system size.