Network synchronization: Spectral versus statistical properties

Fatihcan M. Atay, Türker Biyikoglu, and Jürgen Jost

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Submission date: 24. Oct. 2006
published in: Physica / D, 224 (2006) 1-2, p. 35-41 
DOI number (of the published article): 10.1016/j.physd.2006.09.018
Bibtex
PACS-Numbers: 02.10.Ox, 05.45.Ra, 05.45.Xt, 89.75
Keywords and phrases: synchronization, graph, degree distribution, algebraic connectivity

Abstract:
We consider synchronization of weighted networks, possibly with asymmetrical connections. Focusing on causal relations rather than the observed correlations, we show that the synchronizability of networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation and clustering coefficient, can fail to characterize the synchronizability of networks in terms of causal relations, despite the observed correlations.