+ )i bRt^RIHt^RIHt^RIt^RIHtRR.t R Rlt R Rlt R R lt R t R#) zB Cuthill-McKee ordering of graph nodes to produce sparse matrices )deque) itemgetterN)arbitrary_elementcuthill_mckee_orderingreverse_cuthill_mckee_orderingc#"\P!V4F&p\VPV4V4RjxL K( R#L 5i)aAGenerate an ordering (permutation) of the graph nodes to make a sparse matrix. Uses the Cuthill-McKee heuristic (based on breadth-first search) [1]_. Parameters ---------- G : graph A NetworkX graph heuristic : function, 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 ------- nodes : generator Generator of nodes in Cuthill-McKee ordering. 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)) See Also -------- reverse_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. N)nxconnected_components connected_cuthill_mckee_orderingsubgraph)G heuristiccs&& P/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/utils/rcm.pyrrs8j $ $Q '3AJJqM9MMM(Ms8AA Ac >\\\WR744#)a_Generate an ordering (permutation) of the graph nodes to make a sparse matrix. Uses the reverse Cuthill-McKee heuristic (based on breadth-first search) [1]_. Parameters ---------- G : graph A NetworkX graph heuristic : function, optional Function to choose starting node for RCM algorithm. If None a node from a pseudo-peripheral pair is used. A user-defined function can be supplied that takes a graph object and returns a single node. Returns ------- nodes : generator Generator of nodes in reverse Cuthill-McKee ordering. Examples -------- >>> from networkx.utils import reverse_cuthill_mckee_ordering >>> G = nx.path_graph(4) >>> rcm = list(reverse_cuthill_mckee_ordering(G)) >>> A = nx.adjacency_matrix(G, nodelist=rcm) Smallest degree node as heuristic function: >>> def smallest_degree(G): ... return min(G, key=G.degree) >>> rcm = list(reverse_cuthill_mckee_ordering(G, heuristic=smallest_degree)) See Also -------- cuthill_mckee_ordering Notes ----- The optimal solution the bandwidth reduction is NP-complete [2]_. References ---------- .. [1] E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices, In Proc. 24th Nat. Conf. ACM, pages 157-72, 1969. http://doi.acm.org/10.1145/800195.805928 .. [2] Steven S. Skiena. 1997. The Algorithm Design Manual. Springer-Verlag New York, Inc., New York, NY, USA. )r )reversedlistr)r r s&&rrrHsj D/GH IIc#"Vf \V4pMV!V4pV0p\V.4pV'dVP4pVx\VP \ W,4V, 4\ ^4R7pVUUu.uFwrxVNK p ppVPV 4VPV 4KR#uuppi5i)Nkey) pseudo_peripheral_noderpopleftsorteddegreesetrupdateextend) r r startvisitedqueueparentndndchildrens && rr r s&q)! gG 5'NE  AHHS^g56JqM J"$%"$!A"%x  X &s/CAC B</Cc a\V4p^pTp\P!W4p\VP 44oSV8:dV#SpV3RlVP 44p\ VPV4\^4R7wr6K)c3><"TFwrVS8XgKVxK R#5iN).0r#distls& r )pseudo_peripheral_node..s>['!DAIAA[s  r) rrshortest_path_lengthmaxvaluesitemsminrr)r ulpvsplfarthestdegr-s& @rrrs !A B A %%a+   7  H>SYY[>QXXh'Z];3rr))__doc__ collectionsroperatorrnetworkxrutilsr__all__rrr rr*rrrAs;% #%E F6Nr5Jp" r