Markov chain-based numerical method for degree distributions of growing networks

In this paper, we establish a relation between growing networks and Markov chains, and propose a computational approach for network degree distributions. Using the Barabasi-Albert model as an example, we first show that the degree evolution of a node in a growing network follows a nonhomogeneous Markov chain. Exploring the special structure of these Markov chains, we develop an efficient algorithm to compute the degree distribution numerically with a computation complexity of O(t(2)), where t is the number of time steps. We use three examples to demonstrate the computation procedure and compare the results with those from existing methods.