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Spectra and eigenvectors of scale-free networks

2001
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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bi-directional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around the center, followed by power-law long tails at both spectrum edges. The largest eigenvalue \lambda_1 depends on system size N as \lambda_1 \sim N^{1/4} for large N, and the corresponding eigenfunction is strongly localized at the hub, the vertex with largest

doi:10.1103/physreve.64.051903
pmid:11735964
fatcat:nnwxfncsl5dcfh7eiiunrykwka