Role of Iso-connectivity Topologies in Multi-agent Interactions
For researchers in multi-agent systems, this work provides a theoretical framework for designing flexible network topologies that maintain global connectivity, though the results are incremental and validated only through examples.
This paper explores different network topologies with equal algebraic connectivity (iso-connectivity) in multi-agent systems, showing that such topologies allow reorganization without affecting information exchange. Analytical solutions for finding distinct graphs with identical connectivity are provided, and a zone of no connectivity change in dense graphs is identified.
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.