Modelling Temporal Networks with Markov Chains, Community Structures and Change Points

Abstract

While temporal networks contain crucial information about the evolving systems they represent, only recently have researchers showed how to incorporate higher-order Markov chains, community structure and abrupt transitions to describe them. However, each approach can only capture one aspect of temporal networks, which often are multifaceted with dynamics taking place concurrently at small and large structural scales and also at short and long timescales. Therefore, these approaches must be combined for more realistic descriptions of empirical systems. Here we present two data-driven approaches developed to capture multiple aspects of temporal network dynamics. Both approaches capture short timescales and small structural scales with Markov chains. Whereas one approach also captures large structural scales with communities, the other instead captures long timescales with change points. Using a nonparametric Bayesian inference framework, we illustrate how the multi-aspect approaches better describe evolving systems by combining different scales, because the most plausible models combine short timescales and small structural scales with large-scale structural and dynamical modular patterns or many change points.