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)>= 1/N the scaling parameter deviates from it significantly. For WS small-world networks, in the special region p(r)is an element of[0.05,0.2], typical scale invariance is found. For growing random networks, in the range of theta is an 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 theta is an element of[0.54,1], we have basically delta > 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.