A regional integrated energy system (RIES) is an electricity-centric multi-energy system that can realize the mutual conversion of electricity, heat, cold, and other energy. Through multi-flexible resource interaction and the transaction of multi-investment entities, the efficiency of energy utilization can be improved. To systematize energy-consuming entities and scale photovoltaic-based renewable energy in a distribution network, the energy-consuming behavior, energy-producing schedule, and trading strategy can be coupled. Considering the interaction between the energy-consuming behavior and the uncertainty of distributed photovoltaic output, an optimal operation method for RIES is proposed on the basis of social network theory and an uncertain evolutionary game method in this paper. From the perspective of the operator, the overall profits of RIES are maximized considering the entity characteristics of both the demand and the supply side. A case study shows that the proposed method can ensure the reasonable distribution of profit among the investment entities. A closer social relationship between energy-consuming entities or a lower transaction risk cost of energy-producing entities can increase the overall energy transaction profit.