edge_expansion

edge_expansion(G, S, T=None, weight=None)

Returns the edge expansion between two node sets.

The edge expansion is the quotient of the cut size and the smaller of the cardinalities of the two sets. [1]

Parameters:

GNetworkX graph

Scollection

A collection of nodes in G.

Tcollection

A collection of nodes in G.

weightobject

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

Returns:

number

The edge expansion between the two sets S and T.

See also

boundary_expansion

mixing_expansion

node_expansion

References

[1]

Fan Chung. Spectral Graph Theory. (CBMS Regional Conference Series in Mathematics, No. 92), American Mathematical Society, 1997, ISBN 0-8218-0315-8 <http://www.math.ucsd.edu/~fan/research/revised.html>

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Additional backends implement this function

graphblas : OpenMP-enabled sparse linear algebra backend.