# Max Flow with aggregated edge capacities

I would like to find a solution for a max-flow problem where there is a combined capacity constraint on edges. For example, in the image below, the capacity for edge (1,3) and edge (2,3) should be 1 in total (which means in the max flow, there will be flow through only one of the edges). Any suggestion on what algorithms may solve this problem?
Thanks Ok! I have i an idea, I don't know if it works. So in your example, you want to restrict the total capacity of $$(1,3)$$ and $$(2,3)$$ to be $$1$$. Then create a new vertex $$4$$, connect $$4$$ to $$3$$ with capacity $$1$$ and connect $$1$$ and $$2$$ to $$4$$ with each capacity $$1$$ like in the following picture then bingo! And in general,if you want to restrict the capacity going into a vertex $$v$$, you can create a dummy vertex $$u$$ and connect $$u$$ to $$v$$ with the restrict capacity. Then you can ask all vertices connected to $$v$$ to connect to $$u$$ instead with their respective capacities. Then of course, you apply Ford–Fulkerson algorithm How's that?