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

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