volume

volume(G, S, weight=None)

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:

GNetworkX graph

Scollection

A collection of nodes in G.

weightobject

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

Returns:

number

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

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>

---

Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.