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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

See also

conductance(), cut_size(), edge_expansion(), edge_boundary(), normalized_cut_size()

References

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