Adding a minimal network flow problem example

[sehy1420-art]

Hello POT maintainers,

I’ve been studying the discrete Beckmann minimum-flow problem on a graph. Its primal formulation seeks an edge flow satisfying the prescribed divergence (mass-balance) constraint while minimizing the total edge-weighted flow. Its dual formulation seeks a vertex potential satisfying a gradient constraint. For graph distance costs, the optimal value equals the 1-Wasserstein distance.

I’m considering contributing a Python tutorial or example, possibly under “Other OT Problems.” It could include:

• the primal Beckmann and dual potential formulations;
• the computed 1-Wasserstein distance value, optimal potential vector, and optimal edge-flow matrix;
• plots of the potential and edge flow; and
• numerical checks for flow conservation, the potential constraints, and the primal–dual objective gap.

I would distinguish the edge-flow solution from POT’s standard transport plan. I could also compare the computed distance with POT’s OT solver using shortest-path distances on the graph.

Would this be a useful addition to POT? If so, is there a preferred location or scope for the example?

This would be my first contribution of this kind, so I’d appreciate any guidance on the best format or approach.