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The magnetic Laplacian (H_A) with standard vertex conditions is defined by the closed quadratic form [\nq_A[u]=\\sum_e\\int_e |(-i\\partial_x-A_e)u_e|^2,dx. ]\nA magnetic Cheeger constant is introduced by adding to the usual boundary term the frustration index of the potential on subgraphs. The first point of the paper is that, on a metric graph, this frustration index is exactly a finite dimensional (\\ell^1) flux distance determined by the periods of (A) on cycles. 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