The development of distributed energy resources (DERs) alongside the recent advances in information and communication technology has motivated electricity customers to play a more active role in network operations. The peer-to-peer (P2P) energy trading is a promising answer to this need, in which players can trade directly with each other and the main network via a two-way exchange of power and information. Therefore, this paper presents a P2P energy platform that aims to implement computationally efficient pool-based, semi-decentralized and decentralized clearing mechanisms considering network constraints and privacy preservation. To solve the newly developed pool-based and semi-decentralized/decentralized clearing mechanisms, a particle swarm optimization (PSO) algorithm and an iterative-based heuristic technique are employed, respectively. Simulations are conducted on the IEEE 11-kV, 33-bus distribution network where both dispatchable generations and renewable resources are present. Four types of consumers including agricultural, commercial, domestic, and industrial (ACDI) loads are considered for simulation purposes. Based on the results, several conclusions can be drawn: (i) even though the decentralized mechanism preserves the privacy of customers by eliminating the role of third parties, it does not guarantee network constraints; (ii) the presence of a central entity in the pool-based mechanism keeps the technical envelopes within the standard range; (iii) the semi-decentralized mechanism is the best time-consuming one, and to some extent conserves information security; and, (iv) all these devised methods are superior in terms of computational efficiency compared to a well-known primal-dual gradient method that exists in the literature.