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minimum_cycle_basis(G, weight=None)

Minimum weight means a cycle basis for which the total weight (length for unweighted graphs) of all the cycles is minimum.

Parameters

G : NetworkX Graph
weight: string :

name of the edge attribute to use for edge weights

Returns

A list of cycle lists. Each cycle list is a list of nodes
which forms a cycle (loop) in G. Note that the nodes are not
necessarily returned in a order by which they appear in the cycle

Returns a minimum weight cycle basis for G

See Also

cycle_basis
simple_cycles

Examples

>>> G = nx.Graph()
... nx.add_cycle(G, [0, 1, 2, 3])
... nx.add_cycle(G, [0, 3, 4, 5])
... print([sorted(c) for c in nx.minimum_cycle_basis(G)]) [[0, 1, 2, 3], [0, 3, 4, 5]]

References:

[1] Kavitha, Telikepalli, et al. "An O(m^2n) Algorithm for Minimum Cycle Basis of Graphs." http://link.springer.com/article/10.1007/s00453-007-9064-z [2] de Pina, J. 1995. Applications of shortest path methods. Ph.D. thesis, University of Amsterdam, Netherlands

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

networkx.algorithms.cycles.minimum_cycle_basis

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them


GitHub : /networkx/algorithms/cycles.py#495
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