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Generate an ordering (permutation) of the graph nodes to make a sparse matrix.
Uses the Cuthill-McKee heuristic (based on breadth-first search) .
- 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 Cuthill-McKee ordering.
>>> 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))
The optimal solution the the bandwidth reduction is NP-complete .
 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  Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA.