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Spectral properties of complex networks

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arxiv 0804.1744 v1 pith:2ARNUUY7 submitted 2008-04-10 cond-mat.dis-nn cond-mat.stat-mech

Ginestra Bianconi This is my paper · ORCID
classification cond-mat.dis-nncond-mat.stat-mech
keywords networkscomplexmatrixpropertiesrandomspectraspectraltheory
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We derive the spectral properties of adjacency matrix of complex networks and of their Laplacian by the replica method combined with a dynamical population algorithm. By assuming the order parameter to be a product of Gaussian distributions, the present theory provides a solution for the non linear integral equations for the spectra density in random matrix theory of the spectra of sparse random matrices making a step forward with respect to the effective medium approximation (EMA) . We extend these results also to weighted networks with weight-degree correlations

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  1. Top eigenpair statistics of diluted Wishart matrices

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    For sparse sample covariance matrices X^T X with nonzero-mean weights, the typical largest eigenvalue and top eigenvector component distribution are obtained from replica-based recursive distributional equations solve...

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