Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks

Abstract

By constructing a multicanonical Monte Carlo simulation, we obtain the full probability distribution ρ N (r) of the degree assortativity coefficient r on configuration networks of size N by using the multiple histogram reweighting method. We suggest that ρ N (r) obeys a large deviation principle, , where the rate function I is convex and possesses its unique minimum at , and ξ is an exponent that scales ρ N ’s with N. We show that ξ = 1 for Poisson random graphs, and ξ ⩾ 1 for scale-free networks in which ξ is a decreasing function of the degree distribution exponent γ. Our results reveal that the fluctuations of r exhibit an anomalous scaling with N in highly heterogeneous networks.