Impact of edges for new nodes on scale-free networks

This paper analyses the impact of edges for new nodes on scale-free networks. Although non-stationary average degree distribution of a sub-linerly growing network follows the power law, the stationary average degree distribution of the network does not. This paper proposes a random growth model whose node arrival process is a renewal process and the number of new edges is a random variable with binomial distribution. The result shows that the stationary average degree distribution of the model follows the power law under an appropriate condition, and the condition is found.