networkx.utils.rcm.cuthill_mckee_ordering

cuthill_mckee_ordering(G, heuristic=None)[source]

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

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

Parameters
Ggraph

A NetworkX graph

heuristicfunction, optional

Function to choose starting node for RCM algorithm. If None a node from a pseudo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node.

Returns
nodesgenerator

Generator of nodes in Cuthill-McKee ordering.

Notes

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

References

1

E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-172, 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.

Examples

>>> from networkx.utils import cuthill_mckee_ordering
>>> G = nx.path_graph(4)
>>> rcm = list(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(cuthill_mckee_ordering(G, heuristic=smallest_degree))