Community-based trading structures play important roles in the development of local energy market (LEM). In this paper, a decentralized optimization model for the trading community formation is proposed based on the Lp-box consensus alternating direction method of multipliers (ADMM), where the network features of the physical systems are explicitly represented by power loss and wheeling charging in local and regional trading level, respectively. The framework for multi-level hybrid trading network construction is introduced involving three different trading modes, i.e, traditional trading mode, agent-based trading mode and peer-to-peer (P2P) trading mode, and two hybrid trading networks, namely Traditional trading & Agent based trading (TA) and Traditional trading & Peer-to-peer trading & Agent based trading (TPA), are developed based on the trading community formation results. The corresponding profit allocation schemes are also presented for the TA and TPA hybrid trading networks respectively. A set of complex network indices is applied to analyze the network characteristics of the TA and TPA trading topologies, while the link entropy (LE) index is used to evaluate the edge significance of the communication relationship network in maintaining global connectivity. Finally, the proposed models are validated via a test system with six IEEE 33-bus systems connected through the IEEE 9-bus system. The results show that the agent-based strategy can benefit all entities compared with the SDR and contribution-based strategies, while the REO (renewable energy output)-first strategy proposed for P2P pairing is more stimulating for the selling entities with larger REOs than distance-first mode. In addition, the entities’ prices in the bi-level trading are significantly improved compared with those of the single-level trading both for agent-based trading and P2P trading. The complex index values of TA are all slightly greater than those of TPA, and a feeder with fewer managers is likely to have a larger LE value. The proposed models for trading community formation and trading network formation provide significant means for the development of sustainable LEMs. •A decentralized trading community formation model is proposed for local energy market.•A framework for multi-level hybrid trading network construction is introduced involving different trading modes.•Two hybrid trading networks are developed with the corresponding profit allocation schemes.•A set of complex network indices is applied to analyze the network characteristics of hybrid trading networks and corresponding communication network.