Localization transition on complex networks via spectral statistics

Details Localization transition on complex networks via spectral statistics Localization transition on complex networks via spectral statistics

2005-09-11

arxiv.org/abs/cond-mat/0509275v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

6 pages, expanded introduction and referencess (to appear in PRE)

Scientific paper

10.1103/PhysRevE.72.066123

The spectral statistics of complex networks are numerically studied. The features of the Anderson metal-insulator transition are found to be similar for a wide range of different networks. A metal-insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small. The critical index of the transition corresponds to the mean field expectation. When the connectivity is higher, the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity, though a precise transition cannot be identified. The absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks, resulting in a small diameter even for a large number of sites.

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