Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:A1L-D
Session:
Number:A1L-D2
On Topology of Networked Multi-Agent Systems for Fast Consensus
Kohnosuke Ogiwara, Norikazu Takahashi,
pp.56-59
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
The rate of convergence of a consensus algorithm for networked multi-agent systems is determined by the second smallest eigenvalue of the graph Laplacian. In this paper, we consider the problem of finding undirected graphs maximizing the second smallest eigenvalue of the Laplacian for the given number of nodes and edges. We show that under certain conditions the second smallest eigenvalue of the Laplacian is maximized for some well- known classes of graphs such as the cycle graph, the star graph and the complete bipartite graph.