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reverse_cuthill_mckee_ordering(G, heuristic=None)[source]

Generate an ordering (permutation) of the graph nodes to make a sparse matrix.

Uses the reverse Cuthill-McKee heuristic (based on breadth-first search) [1].

  • G (graph) – A NetworkX graph
  • heuristic (function, optional) – Function to choose starting node for RCM algorithm. If None a node from a psuedo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node.

nodes – Generator of nodes in reverse Cuthill-McKee ordering.

Return type:



>>> from networkx.utils import reverse_cuthill_mckee_ordering
>>> G = nx.path_graph(4)
>>> rcm = list(reverse_cuthill_mckee_ordering(G))
>>> A = nx.adjacency_matrix(G, nodelist=rcm) 

Smallest degree node as heuristic function:

>>> def smallest_degree(G):
...     return min(G, key=G.degree)
>>> rcm = list(reverse_cuthill_mckee_ordering(G, heuristic=smallest_degree))


The optimal solution the the bandwidth reduction is NP-complete [2].


[1]E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-72, 1969. http://doi.acm.org/10.1145/800195.805928
[2]Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA.