edge_current_flow_betweenness_partition#

edge_current_flow_betweenness_partition(G, number_of_sets, *, weight=None)[source]#

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