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Finite-size effects in exponential random graphs
Journal of Complex Networks. 2020. Vol. 8. No. 1. P. cnaa008.
Gorsky A., Valba O. V.
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.
Language:
English
Keywords: случайные графыrandom graphsnetworks, metropolis dynamics, phase transitionфазовые переходы
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