In this paper, we study the H_∞-norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the H_∞-norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the H_∞-norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the H_∞-norm, which is in terms of the algebraic connectivity of the graph on which the distribution network is defined.