TY - JOUR AB - This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space. AU - Erbar, Matthias AU - Forkert, Dominik L AU - Maas, Jan AU - Mugnolo, Delio ID - 11700 IS - 5 JF - Networks and Heterogeneous Media SN - 1556-1801 TI - Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph VL - 17 ER -