How much random a random network is : a random matrix analysis

Details How much random a random network is : a random matrix analysis How much random a random network is : a random matrix analysis

2008-05-28

arxiv.org/abs/0805.4343v1

EPL, 87 (2009) 48010

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in networks. As networks deviate from the regular structure, $\Delta_3$ follows random matrix prediction of linear behavior, in semi-logarithmic scale with the slope of $1/\pi^2$, for the longer scale.

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