Research and Analysis about the Length of Vertex-Degree Sequence of Complex Networks with Poisson Distribution

Degree distribution is an important characteristic of complex networks. To better understand the mechanism of complex networks, it is necessary to analyze their vertex-degree sequences. We had shown before that, for a complex network model with power law distribution or exponential distribution or general degree distribution, the length l of the unequal vertex-degree sequence is of order logN. Poisson distribution is an important distribution in reality. In the present paper, we further study complex networks with Poisson distribution and more general distributions, and prove that the same conclusion holds as well. In addition, we support the conclusion by verifying many real-world network and system examples.