Equitable Partitions in the Controllability of Undirected Signed Graphs

This paper studies the controllability of multi-agent networks with antagonistic interactions, where signed graphs are used to represent such networks. By analyzing and abstracting definitions of equitable partitions of unsigned graphs and signed graphs, new definitions of an equitable partition and an almost equitable partition in the controllability of undirected signed graphs are proposed, which are the natural extension of unsigned graphs. The reasonability of the definitions is discussed in detail. Under this new partition, a new general necessary condition is proposed for controllability of undirected signed graphs.