# Maximum Flow, Minimum Cut, and Shortest Paths

Whenever the edges of a graph are assigned a capacity it is possible to compute the maximum flow and the minimum cut of the graph. Whenever the edges of a graph are assigned a weight it is possible to find shortest paths in the graph. If one wants to perform these computations on a graph where none of its edges have been assigned a capacity or a weight, then the edges are taken to have a capacity or weight of one, and the computations are carried out accordingly.

The flow-based and shortest-paths algorithms and the resulting functionalities are fully documented in Chapter [Multigraphs](../Multigraphs/index-multigraphs.md#multigraph), Sections [Maximum Flow and Minimum Cut](../Networks/flow.md#multigraph-sec-flow) and [Distances, Shortest Paths and Minimum Weight Trees](../Multigraphs/shortest-paths.md#multigraph-sec-shortp) respectively.