# Symmetry-Induced Clustering in Multi-Agent Systems using Network Optimization and Passivity

## TL;DR

This paper investigates how symmetry in network structures influences the formation of clusters in multi-agent systems, demonstrating that certain symmetries lead to predictable clustering behavior and proposing methods to design networks with desired clustering properties.

## Contribution

It introduces a novel link between symmetry properties and clustering in passive multi-agent systems, and proposes a framework for designing networks to achieve specific clustering outcomes.

## Key findings

- Symmetry induces natural clustering in passive multi-agent systems.
- Clusters correspond to exchangeability graph symmetries.
- Method for designing networks to enforce prescribed clustering.

## Abstract

This work studies the effects of a weak notion of symmetry on diffusively-coupled multi-agent systems. We focus on networks comprised of agents and controllers which are maximally equilibrium independent passive, and show that these converge to a clustered steady-state, with clusters corresponding to certain symmetries of the system. Namely, clusters are computed using the notion of the exchangeability graph. We then discuss homogeneous networks and the cluster synthesis problem, namely finding a graph and homogeneous controllers forcing the agents to cluster at prescribed values.