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Deep learning models have emerged in machine learning and related fields, demonstrating astonishing performance in various visual tasks. Despite their great success, however, these models are unable to fully encode intrinsic visual structures, and often ignore the spatial, topological, and semantic information contained within an image. Graph neural networks offer a good framework to face this aspect, but their effective use for visual tasks has been only partly explored and mainly starting from a limited perspective. This work aims to address this gap by conducting a systematic comparison of current graph construction techniques within the context of a fixed three-layer GCN architecture. Through an empirical study, it demonstrates in particular how the network structure affects performance and provides an important methodological contribution regarding the computational stages preceding graph utilization, which will be strongly influenced by the structure itself.