+ j,^Rt^RIt^RIHt.R Ot]!R4]P R44t]!R4]P R Rl44t]!R4]P R44t ]!R4]P R44t ]!R4]P !RR 7R R l44t R#) zStrongly connected components.N)not_implemented_for undirectedc#"\V4pV^8XdR#VPp/p\4p.p.p.p.p^p VEFp W9dK V ^, p T p WV &VPV 4VP\ W*,44VPR4V'gKgVR,p VR,Fp W9dSV ^, p WV &VPV 4VP\ W-,44VPR4KwW9gKcW<,W=,8gKxRVR&W=,W<&W<,V 8XgKW8XgK\V4pVP V4VxR# VP 4VP 4VP 4'daW<,pV 0pV'd6W8R,,V8d"VPVP 44K=VP V4VxEKvVPV 4VR,pVV,W<,8gEKRVR&W<,VV&EK R#5i)aGenerate nodes in strongly connected components of graph. Parameters ---------- G : NetworkX Graph A directed graph. Returns ------- comp : generator of sets A generator of sets of nodes, one for each strongly connected component of G. Raises ------ NetworkXNotImplemented If G is undirected. Examples -------- Generate a sorted list of strongly connected components, largest first. >>> G = nx.cycle_graph(4, create_using=nx.DiGraph()) >>> nx.add_cycle(G, [10, 11, 12]) >>> [ ... len(c) ... for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True) ... ] [4, 3] If you only want the largest component, it's more efficient to use max instead of sort. >>> largest = max(nx.strongly_connected_components(G), key=len) See Also -------- connected_components weakly_connected_components kosaraju_strongly_connected_components Notes ----- Iterative version of Tarjan's algorithm using the improvements described by Tarjan and Zwick in their survey [1]_, plus a trick borrowed from the Rust implementation of the WebGraph framework [2]_. References ---------- .. [1] Robert E. Tarjan and Uri Zwick, "Finding strong components using depth-first search", European Journal of Combinatorics, 119, 2024. https://doi.org/10.1016/j.ejc.2023.103815 .. [2] Tommaso Fontana, Sebastiano Vigna, and Stefano Zacchiroli, "WebGraph: The next generation (is in Rust)", Companion Proceedings of the ACM Web Conference 2024, pp. 686-689, 2024. https://doi.org/10.1145/3589335.3651581 NTF)len_adjsetappenditerupdatepopadd)GNadjlowlink scc_founddfs_vdfs_itdfs_lead comp_stackindexsourceroot_lowvwsccv_lowparents& r/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/algorithms/components/strongly_connected.pystrongly_connected_componentsr sz AAAv &&CGI E FHJ E      V d3;'(eb ABZZ#QJE!&AJLLOMM$sv,/OOD)%'*wz*A#(HRL!(GJzX-%*!*o 5)! ) .  <<>>#JE#C$B)@E)I  01$$S)I%%a("2YFv3', *1*is9BI"A0II,I IAI.IA8I?Ic#6"\\P!VPRR7VR74p\ V4p\ 4pV'd\ V4V8dVP 4pWT9dK0V0pVPV4V.pV'dx\ V4V8dhVP 4pVPV,F>p W9gK VPV 4VPV 4VPV 4K@ KVxKR#R#5i)aGenerate nodes in strongly connected components of graph. Parameters ---------- G : NetworkX Graph A directed graph. source : node, optional (default=None) Specify a node from which to start the depth-first search. If not provided, the algorithm will start from an arbitrary node. Yields ------ set A set of all nodes in a strongly connected component of `G`. Raises ------ NetworkXNotImplemented If `G` is undirected. NetworkXError If `source` is not a node in `G`. Examples -------- Generate a list of strongly connected components of a graph: >>> G = nx.cycle_graph(4, create_using=nx.DiGraph()) >>> nx.add_cycle(G, [10, 11, 12]) >>> sorted(nx.kosaraju_strongly_connected_components(G), key=len, reverse=True) [{0, 1, 2, 3}, {10, 11, 12}] If you only want the largest component, it's more efficient to use `max()` instead of `sorted()`. >>> max(nx.kosaraju_strongly_connected_components(G), key=len) {0, 1, 2, 3} See Also -------- strongly_connected_components Notes ----- Uses Kosaraju's algorithm. F)copy)rN) listnxdfs_postorder_nodesreverserrr r rr ) rrpostnseenrnewstackrrs && r&kosaraju_strongly_connected_componentsr-sd &&qyyey'>> G = nx.DiGraph( ... [(0, 1), (1, 2), (2, 0), (2, 3), (4, 5), (3, 4), (5, 6), (6, 3), (6, 7)] ... ) >>> nx.number_strongly_connected_components(G) 3 See Also -------- strongly_connected_components number_connected_components number_weakly_connected_components Notes ----- For directed graphs only. c3&"TFp^xK R#5i)N).0rs& r 7number_strongly_connected_components..s=>> G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 2)]) >>> nx.is_strongly_connected(G) True >>> G.remove_edge(2, 3) >>> nx.is_strongly_connected(G) False Raises ------ NetworkXNotImplemented If G is undirected. See Also -------- is_weakly_connected is_semiconnected is_connected is_biconnected strongly_connected_components Notes ----- For directed graphs only. z-Connectivity is undefined for the null graph.)rr$NetworkXPointlessConceptnextr r6s&ris_strongly_connectedr<sGX 1v{)) ?   t1!45 6#a& @@r8T) returns_graphcaaVf\P!V4p/o/p\P!4pSVPR&\ V4^8XdV#\ V4F%wopWBS&SP V3RlV44K' S^,pVP\V44VPV3RlVP444\P!W2R4V#)aReturns the condensation of G. The condensation of G is the graph with each of the strongly connected components contracted into a single node. Parameters ---------- G : NetworkX DiGraph A directed graph. scc: list or generator (optional, default=None) Strongly connected components. If provided, the elements in `scc` must partition the nodes in `G`. If not provided, it will be calculated as scc=nx.strongly_connected_components(G). Returns ------- C : NetworkX DiGraph The condensation graph C of G. The node labels are integers corresponding to the index of the component in the list of strongly connected components of G. C has a graph attribute named 'mapping' with a dictionary mapping the original nodes to the nodes in C to which they belong. Each node in C also has a node attribute 'members' with the set of original nodes in G that form the SCC that the node in C represents. Raises ------ NetworkXNotImplemented If G is undirected. Examples -------- Contracting two sets of strongly connected nodes into two distinct SCC using the barbell graph. >>> G = nx.barbell_graph(4, 0) >>> G.remove_edge(3, 4) >>> G = nx.DiGraph(G) >>> H = nx.condensation(G) >>> H.nodes.data() NodeDataView({0: {'members': {0, 1, 2, 3}}, 1: {'members': {4, 5, 6, 7}}}) >>> H.graph["mapping"] {0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1} Contracting a complete graph into one single SCC. >>> G = nx.complete_graph(7, create_using=nx.DiGraph) >>> H = nx.condensation(G) >>> H.nodes NodeView((0,)) >>> H.nodes.data() NodeDataView({0: {'members': {0, 1, 2, 3, 4, 5, 6}}}) Notes ----- After contracting all strongly connected components to a single node, the resulting graph is a directed acyclic graph. mappingc3*<"TFqS3xK R#5iNr1)r2r(is& rr3condensation..s1y!1vysc3z<"TF0wrSV,SV,8wgKSV,SV,3xK2 R#5irAr1)r2urr?s& rr3rCs6-6TQ'!*PQ :R WQZ Ys;;members) r$r DiGraphgraphr enumerater add_nodes_fromrangeadd_edges_fromedgesset_node_attributes)rrrFC componentnumber_of_componentsrBr?s&& @@r condensationrR9s~ {..q1GG A AGGI 1v{!# 9 1y11'q5U/01-.WWY1y1 Hr8)r7r r<r-rRrA) __doc__networkxr$networkx.utils.decoratorsr__all__ _dispatchabler r-r7r<rRr1r8rrXs$9 \"B5#B5J\"A#AH\"$>#$>N\"/A#/Ad\"%P &#P r8