Analysis of the degree distribution of a multi-community consumer-producer network with both growing and rewiring dynamics

Many consumer-producer networks appear with community structure, and evolve with both growing and rewiring dynamics. In the present paper, we analyze a multi-community consumer-producer network model with both growing and rewiring dynamics. The growing rate and rewiring rate in each community evolve with time due to the interacting of communities. We prove that the steady degree distribution in each community of the multi-community consumer-producer network model is equivalent to that in a consumer-producer network model without community structure.