Markov chain-based stability analysis of growing networks

From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.