# Which flow algorithm on a graph is used when the capacity is a rational number?

Does ford fulkerson only use whole numbers? I tried to understand this but without success

Thank you

• There are many network flow algorithms. You may want to clarify whether algorithms other than Ford-Fulkerson algorithm are covered. – John L. Jan 1 '19 at 21:56

Since all steps of the algorithm merely involve addition, you can compute the least common multiple $$m$$ of the denominators of all weights involved, and creating $$G'$$ from $$G$$ by multiplying all weights by $$m$$.
Then all weights are integers and you can run Ford-Fulkerson. You can divide the results from it by $$m$$ again to get back your rationals.