Randomness of random networks: A random matrix analysis

Abstract

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