A discrete Benamou-Brenier formulation of Optimal Transport on graphs

arXiv:2601.04193v2 Announce Type: replace-cross Abstract: We propose a discrete transport equation on graphs which connects distributions on both vertices and edges. We then derive a discrete analogue of the Benamou-Brenier formulation for Wasserstein-$1$ distance on a graph and as a result classify all $W_1$ geodesics on graphs.