Numerical analysis of a network evolution model

Abstract

In this paper we introduce a new network evolution model. The basic feature of the model is the cooperation (interaction) of N nodes. In our model every step m new nodes are born, where m is a discrete random variable with values 0,1, 2,…, N − 1. Then the m new nodes interact with (N − m) old vertices, so that they form a complete graph on N vertices. The old nodes can be chosen either uniformly or by using the preferential attachment rule. We analyze certain properties of the above mentioned model by computer simulations. Power-law degree and weight distributions and clustering coefficients are studied.