Scaling invariance in spectra of complex networks: a diffusion factorial moment approach

A new method called diffusion factorial moment is used to obtain scaling features embedded in the spectra of complex networks. For an Erdos-Renyi network with connecting probability p(ER) < 1/N, the scaling parameter is delta = 0.51, while for p(ER) > or = 1/N the scaling parameter deviates from it significantly. For WS small-world networks, in the special region p(r) element of [0.05,0.2], typical scale invariance is found. For growing random networks, in the range of theta element of [0.33,049], we have delta = 0.6 +.- 0.1. And the value of delta oscillates around delta = 0.6 abruptly. In the range of delta element of [0.54,1], we have basically element of > 0.7. Scale invariance is one of the common features of the three kinds of networks, which can be employed as a global measurement of complex networks in a unified way.