This paper presents algorithms to determine efficient trades in a deregulated electricity market model. In the electricity market model, combination of agents represents four types of market participants: public utilities, independent power producers, retailers, and consumers. By utilizing network flow, our algorithms discover efficient trades satisfying constraints on supply and demand in the electricity market model. Simulation results show the efficiency of trades determined by our algorithm by comparing the social welfare of the determined trades with the maximum social welfare on an electricity market model.