Consensus Speed and Network Topology of Multiagent Systems

This paper gives some new results on relations between consensus speed and network topology of multiagent systems, which are useful for design of the systems. Especially, relations between consensus speed and number of edges, difference of the degree, and number of closed paths are shown in the paper by computing the second smallest eigenvalues of the Laplacian matrices. We also show concrete examples of network topologies with redundant edges, which can be removed without reducing consensus speed.