

Preprint 97/2004
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
Bibtex
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
Abstract:
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.