This paper investigates a fully decentralized model for electricity trading within a transactive energy market. The proposed model presents a peer-to-peer (P2P) trading framework between the clients. The model is incorporated for industrial, commercial, and residential energy hubs to serve their associated demands in a least-cost paradigm. The alternating direction method of multipliers (ADMM) is implemented to address the decentralized power flow in this study. The optimal operation of the energy hubs is modeled as a standard mixed-integer linear programming (MILP) optimization problem. The corresponding decision variables of the energy hubs operation are transferred to the peer-to-peer (P2P) market, and ADMM is applied to ensure the minimum data exchange and address the data privacy issue. Two different scenarios have been studied in this paper to show the effectiveness of the electricity trading model between peers, called integrated and coordinated operation modes. In the integration mode, there is no P2P energy trading while in the coordinated framework, the P2P transactive energy market is taken into account. The proposed model is simulated on the modified IEEE 33-bus distribution network. The obtained results confirm that the coordinated model can efficiently handle the P2P transactive energy trading for different energy hubs, addressing the minimum data exchange issue, and achieving the least-cost operation of the energy hubs in the system. The obtained results show that the total operating cost of the hubs in the coordinated model is lower than that of the integrated model by $590.319, i.e. 11.75 % saving in the costs. In this regard, the contributions of the industrial, commercial, and residential hubs in the total cost using the integrated model are $3441.895, $596.600, and $988.789, respectively. On the other hand, these energy hubs contribute to the total operating cost in the coordinated model by $2932.645, $590.155, and $914.165 respectively. The highest decrease relates to the industrial hub by 14.8 % while the smallest decrease relates to the residential hub by 1 %. Furthermore, the load demand in the integrated and coordinated models is mitigated by 13 % and 17 %, respectively. These results indicate that the presented framework could effectively and significantly reduce the total load demand which in turn leads to reducing the total cost and power losses.