+ j%^RIHt^RIt^RIHtHtRR.t]!R4]P!RRR 7RR l44t R t R t R t R] R] /t ]!R4]P!RRR7RRl44tR#))chainN)not_implemented_forpairwisemetric_closure steiner_treedirectedweightT) edge_attrs returns_graphc 2^RIpVPR\^R7\P!4p\ V4p\P !WR7p\V4wpwrx\V4\V48wdRp \P!V 4hVPV4VF#p VPWjWz,W,R7K% VFBwpwrxVPV4VF#p VPWjWz,W,R7K% KD V#)aReturn the metric closure of a graph. The metric closure of a graph *G* is the complete graph in which each edge is weighted by the shortest path distance between the nodes in *G* . Parameters ---------- G : NetworkX graph Returns ------- NetworkX graph Metric closure of the graph `G`. Notes ----- .. deprecated:: 3.6 `metric_closure` is deprecated and will be removed in NetworkX 3.8. Use :func:`networkx.all_pairs_shortest_path_length` instead. Nzpmetric_closure is deprecated and will be removed in NetworkX 3.8. Use nx.all_pairs_shortest_path_length instead.)category stacklevelr z:G is not a connected graph. metric_closure is not defined.distancepath) warningswarnDeprecationWarningnxGraphsetall_pairs_dijkstranextlen NetworkXErrorremoveadd_edge) Gr rMGnodesall_paths_iterurrmsgvs && n/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/algorithms/approximation/steinertree.pyrr s0 MM 9#   A VF**12_mehlhorn_steiner_tree...aad1gajnnVQ.Gr'keyNmin.0r#r%rr s&@@r& )_mehlhorn_steiner_tree..`s3 13qtAw$GH I5:)rmulti_source_dijkstranodesredgesr0has_edgerr9minimum_spanning_edges shortest_pathrlist is_multigraph edge_subgraphcopy_remove_nonterminal_leaves)rterminal_nodesr distancespathsd_1sr% G_1_primer#r)susv weight_here new_weightG_2G_3_rn1n2G_3_mstG_4sf&f r&_mehlhorn_steiner_treer[As//>&QI C A WWYx{"I  Igg4g( dqtBb'lTXXfa%8832w<G !!"))   r  =[B-*;K*HIJ   r  <) # #ID MC ((*Ca17tnFB LLR"b fa(@L A% 2,,SuVLMG   //' " ' ' )CsN3 99;r'c aa\P!4p\V4pVP4p\P!SVSR7wrg\ S4\ V48wdRp\P !V4hVF#p VPWYWi,Wy,R7K% VP4FXp\P!SVSR7wrgVPV4VF#p VPWYWi,Wy,R7K% KZ \P!VRRR7p \P!RV 44p SP4'dVV3RlV 4p SPV 4p \P!V RR R7p SPV 4P4p\W4VP!4#) )sourcer zG is not a connected graph.rrT)r r)c3L"TFwrp\VR,4xK R#5i)rN)r)r;r#r%ds& r&r<$_kou_steiner_tree..s 'U9a6(;(;9s"$c 3x<aa"TF-wooSS\SS,S,VVVV3RlR73xK/ R#5i)cR<SS,S,V,PS^4#r-r/r1s&r&r3-_kou_steiner_tree...r5r'r6Nr8r:s&@@r&r<r`s3 %13qtAw$GH I%r>r F)rrrpopsingle_source_dijkstrarrrrHrrCr from_iterablerFrGrIrA)rrJr Hunvisited_terminalsr#rKrLr$r% mst_edges mst_all_edgesG_ST_ST_Hsf&f r&_kou_steiner_treernis}  An- !A001VLI 1vY+s##  1),UX >!! % % '44QqP ""1%$A JJqilJ B%())!JTJI'''U9'UUM % //- (C # #Cu EC //#  # # %Cs3 99;r'c a\V4pSUu0uF/p\\SV,4V0, 4^8XgK-VkK1 ppWB, pV'd\P!V3RlV4!pWeV,,pSPV4VUu0uF/p\\SV,4V0, 4^8XgK-VkK1 ppWB, pKR#uupiuupi)r.c3H<"TFp\SV,4xK R#5iN)r)r;nrs& r&r<-_remove_nonterminal_leaves..s&M:LQs1Q4yy:Ls"N)rrunionremove_nodes_from)r terminals terminal_setrrleavesnonterminal_leavescandidate_leavessf& r&rIrIsy>L 8Ac#ad)qc/2a7aaF 8. 99&M:L&MN== ./-K-S1Y!_1E1J!!-K#2 9Ls*CC*C" C"koumehlhorn)preserve_all_attrsr caaVfRp\V,pT!STS4pSP4'dTT3RlT4pSP T4pT# \dp\T R24ThRp?ii;i)um Return an approximation to the minimum Steiner tree of a graph. The minimum Steiner tree of `G` w.r.t a set of `terminal_nodes` (also *S*) is a tree within `G` that spans those nodes and has minimum size (sum of edge weights) among all such trees. The approximation algorithm is specified with the `method` keyword argument. All available algorithms produce a tree whose weight is within a ``(2 - (2 / l))`` factor of the weight of the optimal Steiner tree, where ``l`` is the minimum number of leaf nodes across all possible Steiner trees. * ``"kou"`` [2]_ (runtime $O(|S| |V|^2)$) computes the minimum spanning tree of the subgraph of the metric closure of *G* induced by the terminal nodes, where the metric closure of *G* is the complete graph in which each edge is weighted by the shortest path distance between the nodes in *G*. * ``"mehlhorn"`` [3]_ (runtime $O(|E|+|V|\log|V|)$) modifies Kou et al.'s algorithm, beginning by finding the closest terminal node for each non-terminal. This data is used to create a complete graph containing only the terminal nodes, in which edge is weighted with the shortest path distance between them. The algorithm then proceeds in the same way as Kou et al.. Parameters ---------- G : NetworkX graph terminal_nodes : list A list of terminal nodes for which minimum steiner tree is to be found. weight : string (default = 'weight') Use the edge attribute specified by this string as the edge weight. Any edge attribute not present defaults to 1. method : string, optional (default = 'mehlhorn') The algorithm to use to approximate the Steiner tree. Supported options: 'kou', 'mehlhorn'. Other inputs produce a ValueError. Returns ------- NetworkX graph Approximation to the minimum steiner tree of `G` induced by `terminal_nodes` . Raises ------ NetworkXNotImplemented If `G` is directed. ValueError If the specified `method` is not supported. NetworkXError If ``method=kou`` and `G` is not connected KeyError If ``method=mehlhorn``, `G` is not connected, and there is not at least one terminal node in every component. Notes ----- For multigraphs, the edge between two nodes with minimum weight is the edge put into the Steiner tree. The ``mehlhorn`` method supports graphs with multiple components, so long as there is at least one terminal node in each component. References ---------- .. [1] Steiner_tree_problem on Wikipedia. https://en.wikipedia.org/wiki/Steiner_tree_problem .. [2] Kou, L., G. Markowsky, and L. Berman. 1981. ‘A Fast Algorithm for Steiner Trees’. Acta Informatica 15 (2): 141–45. https://doi.org/10.1007/BF00288961. .. [3] Mehlhorn, Kurt. 1988. ‘A Faster Approximation Algorithm for the Steiner Problem in Graphs’. Information Processing Letters 27 (3): 125–28. https://doi.org/10.1016/0020-0190(88)90066-X. 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