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

Abstract

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.

References in corpus (4)

• Random matrix analysis of complex networks
• Random matrix analysis of network Laplacians
• Spectral transitions in networks
• Spectral densities of scale-free networks

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