# networkx.algorithms.cuts.cut_size¶

cut_size(G, S, T=None, weight=None)[source]

Returns the size of the cut between two sets of nodes.

A cut is a partition of the nodes of a graph into two sets. The cut size is the sum of the weights of the edges “between” the two sets of nodes.

Parameters
GNetworkX graph
Scollection

A collection of nodes in `G`.

Tcollection

A collection of nodes in `G`. If not specified, this is taken to be the set complement of `S`.

weightobject

Edge attribute key to use as weight. If not specified, edges have weight one.

Returns
number

Total weight of all edges from nodes in set `S` to nodes in set `T` (and, in the case of directed graphs, all edges from nodes in `T` to nodes in `S`).

Notes

In a multigraph, the cut size is the total weight of edges including multiplicity.

Examples

In the graph with two cliques joined by a single edges, the natural bipartition of the graph into two blocks, one for each clique, yields a cut of weight one:

```>>> G = nx.barbell_graph(3, 0)
>>> S = {0, 1, 2}
>>> T = {3, 4, 5}
>>> nx.cut_size(G, S, T)
1
```

Each parallel edge in a multigraph is counted when determining the cut size:

```>>> G = nx.MultiGraph(["ab", "ab"])
>>> S = {"a"}
>>> T = {"b"}
>>> nx.cut_size(G, S, T)
2
```