# Cut (graph theory)

## Partition of a graph's nodes into 2 disjoint subsets / From Wikipedia, the free encyclopedia

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In graph theory, a **cut** is a partition of the vertices of a graph into two disjoint subsets.[1] Any cut determines a **cut-set**, the set of edges that have one endpoint in each subset of the partition. These edges are said to **cross** the cut. In a connected graph, each cut-set determines a unique cut, and in some cases cuts are identified with their cut-sets rather than with their vertex partitions.

In a flow network, an **s–t cut** is a cut that requires the *source* and the *sink* to be in different subsets, and its *cut-set* only consists of edges going from the source's side to the sink's side. The *capacity* of an s–t cut is defined as the sum of the capacity of each edge in the *cut-set*.

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