Finite-size effects in exponential random graphs

In this article, we shownumerically the strong finite-size effects in exponential random graphs. Particularly, for the two-star model above the critical value of the chemical potential for triplets a ground state is a starlike graph with the finite set of hubs at network density p < 0.5 or as the single cluster at p > 0.5. We find that there exists the critical value of number of nodes N* (p) when the ground state undergoes clear-cut crossover. At N > N* (p), the network flows via a cluster evaporation to the state involving the small star in the Erdos-Renyi environment. The similar evaporation of the cluster takes place at N > N * (p) in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.