MARKOV CHAIN-BASED ANALYSIS OF THE DEGREE DISTRIBUTION FOR A GROWING NETWORK

In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of 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.     

Markov chain-based analysis of a modified Cooper-Frieze model

From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the exis- tence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.