Maximum entropy in dynamic complex networks

Abstract

The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However, information-theoretic randomisation methods with well-established foundations mostly provide a stationary description of these systems, while stochastic randomisation methods that account for their dynamic nature lack such general foundations and require extensive repetition of the stochastic process to measure statistical properties. In this work, we extend the applicability of information-theoretic methods beyond stationary network models. By using the information-theoretic principle of maximum caliber we construct dynamic network ensemble distributions based on constraints representing statistical properties with known values throughout the evolution. We focus on the particular cases of dynamics constrained by the average number of connections of the whole network and each node, comparing each evolution to simulations of stochastic randomisation that obey the same constraints. We find that ensemble distributions estimated from simulations match those calculated with maximum caliber and that the equilibrium distributions to which they converge agree with known results of maximum entropy given the same constraints. Finally, we discuss further the connections to other maximum entropy approaches to network dynamics and conclude by proposing some possible avenues of future research.