Finite-size effects in exponential random graphs and cluster evaporation
Abstract
In this Letter we find numerically the strong finite-size effects in the critical behavior of Erdos-R\'enyi (ER) networks supplemented with chemical potentials for some motifs, in particular 2-stars and triangles. For the 2-star model above the critical value of the chemical potential a ground state looks as star-like graph with the finite set of hubs at ER parameter p<0.5 or as the single cluster at p>0.5. It is found that there exists the critical value of number of nodes N*(p) when the ground state undergoes clear-cut crossover and at N>N*(p) the network flows via a cluster evaporation to the state involving the small star in the ER 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. The possible analogies concerning the strong entropic finite-size effects in the holographic description of matrix black hole (BH) formation and evaporation are mentioned.