Spectral densities of scale-free networks

Abstract

The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and $\beta$.

arXiv comment14 pages, two figures

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• Spectral Properties of Directed Random Networks with Modular Structure
• Spectral analysis of deformed random networks
• Measuring the dimension of partially embedded networks
• Spectral Density of Complex Networks with Two Species of Nodes
• The normalized Laplacian spectrum and eigentime identities of hype-cubes