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Many authors emphasize the importance of market structure in the definition of financial fragility; however, a study estimating the degree of completeness and heterogeneity of specific markets is still missing. In this paper, we address this issue. The paper contributes to the contagion literature by proposing measures of completeness and concentration degrees or heterogeneity amongst financial markets. Besides the essentially methodological contribution, we present some empirical results for the Brazilian interbank market.