Clusters in multi-leader directed consensus networks

Abstract

We study clustering properties of networks of singleintegrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge weights, and initial values. Focusing on the interaction topology of the network, we introduce the notion of topological clusters, which are sets of nodes that converge to an identical value due to the topological characteristics of the network, independent of the value of the edge weights. We then investigate properties of topological clusters and present a necessary and sufficient condition for a set of nodes to form a topological cluster. We also provide an algorithm for finding topological clusters. Examples show the validity of the analysis and algorithm.