In this paper, the feasibility of peer-to-peer (P2P) energy trading in a voltage-constrained grid-connected network is studied. In particular, a local voltage management scheme is proposed that takes network constraints into consideration to instruct the prosumers to trade energy frequently in the P2P market. A coalition graph game-based P2P energy trading framework is developed, in which prosumers can form the coalition to negotiate and decide on the energy trading parameters, such as trading quantities and prices. The Myerson value rule is used to allocate the total payoff of the proposed game fairly among the participating prosumers. Further, the stability of the proposed coalition structure is confirmed. Several simulation results are provided to verify the effectiveness of the developed P2P trading model. The simulation results show that the proposed P2P trading framework can enable prosumers to export power without causing high voltage problem in the network, and help prosumers cut down a significant portion of their overall electricity costs compared to the feed-in-tariff and coalition game model without mutual negotiations.