  This paper establishes a relation between scale-free networks and Markov
chains, and proposes a computation framework for degree distributions of
scale-free networks. We first find that, under the BA model, the degree
evolution of individual nodes in a scale-free network follows some
non-homogeneous Markov chains. Exploring the special structure of these Markov
chains, we are able to develop an efficient algorithm to compute the degree
distribution numerically. The complexity of our algorithm is O(t^2), where $t$
is the number of time steps for adding new nodes. We use three examples to
demonstrate the computation procedure and compare the results with those from
the existing methods.
