Some New Statistics on Determine Network Models

Abstract

In order to make it easier to study the scale-free nature of the complex network, and to explore the topological structures of networks by mathematical methods. There are many successful mathematical methods shown in scale-free networks that are forming branches of mathematics and network science. We are motivated from the cumulative degree distribution and edge cumulative degree distribution of scale-free networks, re-designed several new methods of cumulative distribution to depict the networks. In this paper, two known networks as an example to illustrate, and prove the equivalence of several new formula, provides more methods for future research.