Topological Clusters in Multi-Agent Networks: Analysis and Algorithm

TL;DR

This paper introduces the concept of topological clusters in multi-agent networks, providing conditions and an algorithm to identify node groups that converge to identical values based solely on network topology.

Contribution

It defines topological clusters, establishes their properties, and presents a novel algorithm for detecting these clusters in directed networks.

Findings

Topological clusters depend only on network topology, not edge weights.

A necessary and sufficient condition for topological clustering is derived.

An effective algorithm for identifying topological clusters is proposed.

Abstract

We study clustering properties of networks of single integrator 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.