edge_current_flow_betweenness_partition

edge_current_flow_betweenness_partition(G, number_of_sets, *, weight=None)

Partition created by removing the highest edge current flow betweenness edge.

This algorithm works by calculating the edge current flow betweenness for all edges and removing the edge with the highest value. It is then determined whether the graph has been broken into at least number_of_sets connected components. If not the process is repeated.

Parameters:

GNetworkX Graph, DiGraph or MultiGraph

Graph to be partitioned

number_of_setsint

Number of sets in the desired partition of the graph

weightkey, optional (default=None)

The edge attribute key to use as weights for edge current flow betweenness calculations

Returns:

Clist of sets

Partition of G

Raises:

NetworkXError

If number_of_sets is <= 0 or number_of_sets > len(G)

See also

edge_betweenness_partition

Notes

This algorithm is extremely slow, as the recalculation of the edge current flow betweenness is extremely slow.

References

[1]

Santo Fortunato ‘Community Detection in Graphs’ Physical Reports Volume 486, Issue 3-5 p. 75-174 http://arxiv.org/abs/0906.0612

Examples

>>> G = nx.karate_club_graph()
>>> part = nx.community.edge_current_flow_betweenness_partition(G, 2)
>>> {0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 16, 17, 19, 21} in part
True
>>> {8, 14, 15, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33} in part
True