Thermodynamic characterization of temporal networks

Abstract

Time-evolving networks have proven to be an efficient and effective means of concisely characterising the behaviour of complex systems over time. However, the analysis of such networks and the identification of the underlying dynamical process has proven to be a challenging problem, particularly trying to model the large-scale properties of graphs. In this paper we present a novel method to characterize the behaviour of the evolving systems based on a thermodynamic framework for graphs. This framework aims at relating the major structural changes in time evolving networks to thermodynamic phase transitions. This is achieved by relating the thermodynamics variables to macroscopic changes in network topology. First, by considering a recent quantum-mechanical characterization of the structure of a network, we derive the network entropy. Then we adopt a Schrödinger picture of the dynamics of the network, in order to obtain a measure of energy exchange through the estimation of a hidden time-varying Hamiltonian from the data. Experimental evaluations on real-world data demonstrate how the estimation of this time-varying energy operator strongly characterizes the different states of time evolving networks.