Algorithmic Renormalization for Network Dynamics

The aim of this work is to give a full, elementary exposition of a recently introduced algorithmic technique for renormalizing dynamic networks. The motivation is the analysis of time-varying graphs. We begin by showing how an arbitrary sequence of graphs over a fixed set of nodes can be parsed so as to capture hierarchically how information propagates across the nodes. Equipped with parse trees, we are then able to analyze the dynamics of averaging-based multiagent systems. We investigate the case of diffusive influence systems and build a renormalization framework to help resolve their long-term behavior. Introduced as a generalization of the Hegselmann-Krause model of multiagent consensus, these systems allow the agents to have their own, distinct communication rules. We formulate new criteria for the asymptotic periodicity of such systems.