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Structure learning is a crucial component of a multivariate Estimation of Distribution algorithm. It is the part which determines the interactions between variables in the probabilistic model, based on analysis of the fitness function or a population. In this paper we take three different approaches to structure learning in an EDA based on Markov networks and use measures from the information retrieval community (precision, recall and the F-measure) to assess the quality of the structures learned. We then observe the impact that structure has on the fitness modelling and optimisation capabilities of the resulting model, concluding that these results should be relevant to research in both structure learning and fitness modelling.