Model reduction of consensus networks by graph simplification

In this paper we consider the problem of approximating a consensus network by a less complex network, by removing cycles from the original network graph. The consensus network consists of agents that exchange relative state information with their neighbors in the network. We assume the agents have single-integrator dynamics and the network graph is undirected. The network used to approximate the original system has the same nodes as the original graph, but its edge set is a strict subset of the original edge set. We obtain a priori upper bounds on the absolute approximation error, depending on the length of the removed cycles, the algebraic connectivity of a chosen spanning tree of the network graph, and the largest eigenvalue of the Laplacian matrix of that spanning tree.