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Spectral analysis and the dynamic response of complex networks.

Authors
  • de Aguiar, M A M
  • Bar-Yam, Y
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Jan 01, 2005
Volume
71
Issue
1 Pt 2
Pages
16106–16106
Identifiers
PMID: 15697657
Source
Medline
License
Unknown

Abstract

The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density rho(lambda) of this matrix reveals important network characteristics: random networks follow Wigner's semicircular law whereas scale-free networks exhibit a triangular distribution. In this paper we show that the spectral density of hierarchical networks follows a very different pattern, which can be used as a fingerprint of modularity. Of particular importance is the value rho(0), related to the homeostatic response of the network: it is maximum for random and scale-free networks but very small for hierarchical modular networks. It is also large for an actual biological protein-protein interaction network, demonstrating that the current leading model for such networks is not adequate.

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