Abstract: 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 existence 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.

Key words: growing networks, preferential attachment, power law