minimum_cycle_basis(G, weight=None)[source]#

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.

GNetworkX Graph
weight: string

name of the edge attribute to use for edge weights

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


>>> G = nx.Graph()
>>> nx.add_cycle(G, [0, 1, 2, 3])
>>> nx.add_cycle(G, [0, 3, 4, 5])
>>> nx.minimum_cycle_basis(G)
[[5, 4, 3, 0], [3, 2, 1, 0]]

[1] Kavitha, Telikepalli, et al. “An O(m^2n) Algorithm for Minimum Cycle Basis of Graphs.” [2] de Pina, J. 1995. Applications of shortest path methods. Ph.D. thesis, University of Amsterdam, Netherlands