h`SrSSKJr SSKJr SSKrSSKJr SS/r S S jr S S jr S S jr S r g)zB Cuthill-McKee ordering of graph nodes to produce sparse matrices )deque) itemgetterN)arbitrary_elementcuthill_mckee_orderingreverse_cuthill_mckee_orderingc## [R"U5H&n[URU5U5ShvN M( gN 7f)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 D/var/www/html/env/lib/python3.13/site-packages/networkx/utils/rcm.pyrrs8j $ $Q '3AJJqM9MMM(Ms8AA Ac 8[[[XS955$)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)rrs rrrHsj D/GH IIc#~# Uc [U5nOU"U5nU1n[U/5nU(aUR5nUv [UR [ X5U- 5[ S5S9nUVVs/sHupxUPM n nnURU 5 URU 5 U(aMggs snnf7f)Nkey) pseudo_peripheral_noderpopleftsorteddegreesetrupdateextend) rrstartvisitedqueueparentndndchildrens rr r s&q)! gG 5'NE  AHHS^g56JqM J"$%"$!A"%x  X %&sA7B=9B7,B=5B=c*^[U5nSnUn[[R"X55n[ UR 55mTU::aU$TnU4SjUR 55n[URU5[S5S9up6M)Nrc3<># UHupUT:XdM Uv M g7fN).0r&distls r )pseudo_peripheral_node..s>['!DAIAA[s  rr) rdictr shortest_path_lengthmaxvaluesitemsminrr)rulpvsplfarthestdegr/s @rrrs !A B A 2**101   7  H>SYY[>QXXh'Z]; rr+)__doc__ collectionsroperatorrnetworkxr utilsr__all__rrr rr,rrrDs;% #%E F6Nr5Jp" r