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The metabolic networks are very well characterized for bacterial such of E.coli. For this reason they provide a a very interesting framework for the construction of analytically tractable statistical mechanics models. In this paper we introduce a solvable model for the distribution of fluxes in the metabolic network. We show that the effect of the topology on the distribution of fluxes is to allow for large fluctuations of their values, a fact that should have implications on the robustness of the system.