Accelerating Consensus by Spectral Clustering and Polynomial Filters

It is known that polynomial filtering can accelerate the convergence towards average consensus on an undirected network. In this paper the gain of a second-order filtering is investigated. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner is proposed to adapt the undirected weights of any given graph to achieve fastest convergence with the polynomial filter. The corresponding cost function differs from the traditional spectral gap, as it favors grouping the eigenvalues in two clusters. A possible loss of robustness of the polynomial filter is also highlighted

The Total s-Energy of a Multiagent System

We introduce the "total s-energy" of a multiagent system with time-dependent links. This provides a new analytical lens on bidirectional agreement dynamics, which we use to bound the convergence rates of dynamical systems for synchronization, flocking, opinion dynamics, and social epistemology