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Finite-size effects in exponential random graphs
In this article, we show numerically 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 star-like graph with the finite set of hubs at network density p<0.5p<0.5 or as the single cluster at p>0.5p>0.5. We find that there exists the critical value of number of nodes N∗(p)N∗(p) when the ground state undergoes clear-cut crossover. At N>N∗(p),N>N∗(p), the network flows via a cluster evaporation to the state involving the small star in the Erdős–Rényi environment. The similar evaporation of the cluster takes place at N>N∗(p)N>N∗(p) in the Strauss model. We suggest that the entropic trap mechanism is relevant for microscopic mechanism behind the crossover regime.