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

We analyze complex networks under random matrix theory framework. Particularly, we show that $Δ_3$ 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, $Δ_3$ follows random matrix prediction of linear behavior, in semi-logarithmic scale with the slope of $1/π^2$, for the longer scale.

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