Graph operations and synchronization of complex networks
Fatihcan M. Atay and Türker Biyikoglu
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Submission date: 27. Dec. 2004
published in: Physical review / E, 72 (2005) 1.2, art-no. 016217
DOI number (of the published article): 10.1103/PhysRevE.72.016217
MSC-Numbers: 05C50, 05C90
PACS-Numbers: 02.10.Ox, 05.45.Ra, 05.45.Xt, 89.75.-k
Keywords and phrases: synchronization, networks, Laplacian, eigenvalue, graph operations
The effects of graph operations on the synchronization of coupled dynamical systems are studied. The operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones. Methods from graph theory are used to calculate or estimate the eigenvalues of the Laplacian operator, which determine the synchronizability of continuous or discrete time dynamics evolving on the network. Results are applied to explain numerical observations on random, scale-free, and small-world networks. An interesting feature is that, when two networks are combined by adding links between them, the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved.