minimum_cycle_basis

minimum_cycle_basis(G, weight=None)

Returns a minimum weight cycle basis for G

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

Parameters

GNetworkX 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

See also

simple_cycles, cycle_basis

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