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A flow \(f: \;V x V \rightarrow R\) is a real-valued function representing the rate of flow between u and v, constrained by the following:

f(u,v) $\leq$ c(u,v)

f(u,v) = -f(v,u)

For every u $\in$ V - {s,t}, \(\sum_{v \in V}
f(u,v) \;=\; 0\).
The total flow into and out of a vertex u is 0.

The value of f(u,v) is the net flow from vertex u to vertex v.

Note that if (u,v) and (v,u) \(\not \in\) E, then f(u,v) = f(v,u) = 0.

The value of a flow f is \(\mid f \mid \;=\; \sum_{v \in V} f(s,v)\).

Copyright © 1998 The University of Texas at Arlington