Network synchronizability analysis: The theory of subgraphs and complementary graphs

In this paper, subgraphs and complementary graphs are used to analyze network synchronizability. Some sharp and attainable bounds are derived for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the network's corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs. (C) 2007 Elsevier B.V. All rights reserved.