11,684 research outputs found
Deformed Gaussian Orthogonal Ensemble description of Small-World networks
The study of spectral behavior of networks has gained enthusiasm over the
last few years. In particular, Random Matrix Theory (RMT) concepts have proven
to be useful. In discussing transition from regular behavior to fully chaotic
behavior it has been found that an extrapolation formula of the Brody type can
be used. In the present paper we analyze the regular to chaotic behavior of
Small World (SW) networks using an extension of the Gaussian Orthogonal
Ensemble. This RMT ensemble, coined the Deformed Gaussian Orthogonal Ensemble
(DGOE), supplies a natural foundation of the Brody formula. SW networks follow
GOE statistics till certain range of eigenvalues correlations depending upon
the strength of random connections. We show that for these regimes of SW
networks where spectral correlations do not follow GOE beyond certain range,
DGOE statistics models the correlations very well. The analysis performed in
this paper proves the utility of the DGOE in network physics, as much as it has
been useful in other physical systems.Comment: Replaced with the revised version, accepted for publication in Phys.
Rev.
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