Role of Iso-connectivity Topologies in Multi-agent Interactions

TL;DR

This paper investigates iso-connectivity topologies in multi-agent systems, providing analytical methods to identify different network configurations with identical connectivity, and explores how agents can move without affecting overall network connectivity.

Contribution

It introduces analytical solutions for determining distinct graphs with the same connectivity and identifies zones where agent movement does not alter global connectivity.

Findings

Multiple iso-connectivity graphs can be analytically determined.

A zone exists where agent movement does not affect connectivity.

Validation through examples confirms the analytical solutions.

Abstract

In this paper, we present the benefits of exploring different topologies with equal connectivity measure, or iso-connectivity topologies, in relation to the multiagent system dynamics. The level of global information sharing ability among agents in a multi-agent network can be quantified by a connectivity measure, called as the Algebraic Connectivity of the associated graph consisting of point-mass agents as nodes and inter-connection links between them as edges. Distinct topologies with the same connectivity play profound role in multi-agent dynamics as they offer various ways to reorganize agents locations according to the requirement during a cooperative mission, without sacrificing the information exchange capability of the entire network. Determination of the distinct multi-agent graphs with identical connectivity is a multimodal problem, in other words, there exist multiple graphs that share the same connectivity. We present analytical solutions of determining distinct graphs with identical connectivity. A family of isospectral graphs are found out by utilizing an appropriate similarity transformation. Moreover, a zone of no connectivity change in a dense graph is unraveled where an agent can move freely without causing any change in the global connectivity. The proposed solutions are validated with the help of sufficient examples.