Abstract: In previous papers, the stationary distributions of a class of discrete and continuous time random graph processes with state space consisting of the simple and directed graphs on N venices were studied. In this paper, the random graph graph process is extended one impotent step further by allowing interaction of edges. Similarly, We obtha the expressions of the stationary distributions and prove that the process is ergodic under different editions.

Key words: Random graph prooes, Minimum Q-process, Stationary distribution, Ergodicity