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Results of a detailed numerical analysis of an n-heptane/air edge flame are presented. The equations of a low-Mach number reacting flow are solved in a two-dimensional domain using detailed models for species transport and chemical reactions. The reaction mechanism involves 560 species and 2538 reversible reactions. We consider an edge flame that is established in a mixing layer with a uniform velocity field. The mixing layer spans the equivalence ratios between pure air and 3.5. The detailed model enables us to analyze the chemical structure of the n-heptane edge flame. We identify major species profiles, discuss reactions causing the heat-release, and exploit Computational Singular Perturbation (CSP) to discuss the main fuel-consumption pathways and the structure of explosive modes in the edge flame. This analysis is performed for several regions in the edge flame to discuss the different processes at work in the premixed branches and the trailing diffusion flame. We compare different cuts through the 2D edge flame to canonical 1D premixed and diffusion flames. We also analyze the accuracy of a skeletal mechanism which was previously developed using CSP from homogeneous ignition calculations of n-heptane and show that a significant reduction in size of the mechanism can be achieved without a significant decrease in accuracy of the edge flame computation. This skeletal mechanism is then used to study the effects of increasing the equivalence ratio in the partially-premixed fuel stream.