Flow Networks

A flow network G = (V, E) is a directed graph where each edge (u,v) $\in$E has capacity c(u,v) $\geq$ 0.

If (u,v) E, then c(u,v) = 0.

Distinguish source (s $\in$ V) and sink (t $\in$ V) as the vertices between which the flow is to be maximized.

• in-degree(s) = 0
• out-degree(t) = 0

For every v $\in$ V, v is on a path from s to t. , therefore the graph is connected.