# Maximum Flow¶

Finding a maximum flow: What is the maximum amount of flow we can send from a node to another node?

The input for problem is directed, weighted graph that contains two special nodes: the $\text{source}$ is a node with no incoming edges, and the $\text{sink}$ is a node with no outgoing edges.

in the maximum flow problem, our task is to send as much flow as possible from the source to the sink.

The weight of each edge is a capacity that restricts the flow that can go through the edge. In each intermediate node, the incoming and outgoing flow has to be equal.