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Market power (MP) analysis under network constraints is a specific feature of electricity markets and, as well, one of the major concerns of the regulators. The goal, in the analysis, is to assess the impacts of network constraints on the market outcomes because of the strategic behaviour of the producers that may or may not take advantage of the knowledge of the network structure and of the constraints. In this work, different factors to the MP that can be used by the strategies of the producers are studied and the impacts of the network constraints in providing additional opportunities to exert MP are considered. The ex-ante analysis of the market is undertaken resorting to a supply function equilibrium (SFE) for which the authors propose a new approach for deriving the best slope for slope bidding strategy by an equivalent intercept iteration method. A set of indices, specifically devised for considering network impacts, are proposed to assess the MP of the producers in a constrained market. The application of the proposed approach is shown and tested on an IEEE 30 bus system.