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In electricity markets, a pool trading model with a power exchange pool is a typical market organization that attracts much more attention than a bilateral trading model. To date, quite a few papers have focused on bilateral trading models, particularly those under network constraints. This trend is due to the model's complexity in terms of the various trading patterns, reflecting the self-interested behavior of the market participants striving to find potentially profitable transactions. In this paper, we propose a new approach based on complex networks suitable for assessing different aspects of bilateral market. This work strives to analyze the bilateral trading patterns in the electricity markets where physical network constraints need to be considered for the feasible and secure operation of the power systems. The goal of the work is to find the stable network structures that can be used to anticipate possible bilateral transactions in the real market place and to provide a novel and applicable approach to studying the bilateral model in electricity markets. The proposed approach has been tested on several test systems in which the transmission network structure of the market that accommodates the transactions is considered. The proposed model is illustrated with examples using a four-bus test system, the IEEE 30-bus, and the IEEE 118-bus test systems.