# networkx.algorithms.cuts.volume¶

volume(G, S, weight=None)[source]

Returns the volume of a set of nodes.

The volume of a set S is the sum of the (out-)degrees of nodes in S (taking into account parallel edges in multigraphs). [1]

Parameters
• G (NetworkX graph)

• S (sequence) – A sequence of nodes in G.

• weight (object) – Edge attribute key to use as weight. If not specified, edges have weight one.

Returns

The volume of the set of nodes represented by S in the graph G.

Return type

number

References

1

David Gleich. Hierarchical Directed Spectral Graph Partitioning. <https://www.cs.purdue.edu/homes/dgleich/publications/Gleich%202005%20-%20hierarchical%20directed%20spectral.pdf>