Cliques and duplication-divergence network growth.

A population of complete subgraphs or cliques in a protein network model is studied. The network evolves via duplication and divergence supplemented with linking a certain fraction of target-replica vertex pairs. We derive a clique population distribution, which scales linearly with the size of the network and is in a perfect agreement with numerical simulations. Fixing both parameters of the model so that the number of links and abundance of triangles are equal to those observed in the fruitfly protein-binding network, we precisely predict the 4- and 5-clique abundance. In addition, we show that such features as fat-tail degree distribution, various rates of average degree growth and nonaveraging, revealed recently for a particular case of a completely asymmetric divergence, are present in a general case of arbitrary divergence.