New exponential law for real networks

Abstract

In this article we have shown that the distributions of ksi satisfy an exponential law for real networks while the distributions of ksi for random networks are bell-shaped and closer to the normal distribution. The ksi distributions for Barabasi-Albert and Watts-Strogatz networks are similar to the ksi distributions for random networks (bell-shaped) for most parameters, but when these parameters become small enough, the Barabasi-Albert and Watts-Strogatz networks become more realistic with respect to the ksi distributions.