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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.

  • G (NetworkX 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()
>>> G.add_cycle([0,1,2,3])
>>> G.add_cycle([0,3,4,5])
>>> print(nx.minimum_cycle_basis(G))
[[0, 1, 2, 3], [0, 3, 4, 5]]


[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