Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2004-06-18
Phys. Rev. E71 (2005) 16106
Nonlinear Sciences
Adaptation and Self-Organizing Systems
4 pages 14 figures
Scientific paper
10.1103/PhysRevE.71.016106
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 follow 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.
Bar-Yam Yaneer
de Aguiar Marcus A. M.
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