9j&VSrSSKrSSKJr /SQr\"S5\R S55r\"S5\R S Sj55r\"S5\R S55r \"S5\R S 55r \"S5\R "S S 9S S j55r g)zStrongly connected components.N)not_implemented_for)$number_strongly_connected_componentsstrongly_connected_componentsis_strongly_connected&kosaraju_strongly_connected_components condensation undirectedc#$# 0n0n[5n/nSnUVs0sHof[URU5_M nnUGHFnX;dM U/n U (dMU SnXa;a US-nXQU'Sn XvHn X;dM U RU 5 Sn O U (aXX&'URUH<n X;dM XX:a[ X&X+/5X&'M)[ X&X/5X&'M> U R 5 X&X:XadU1n U(aDXSX:a7UR 5n U R U 5 U(aXSX:aM7URU 5 U v OURU5 U (aGM/GMI gs snf7f)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 ----- Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_. Nonrecursive version of algorithm. References ---------- .. [1] Depth-first search and linear graph algorithms, R. Tarjan SIAM Journal of Computing 1(2):146-160, (1972). .. [2] On finding the strongly connected components in a directed graph. E. Nuutila and E. Soisalon-Soinen Information Processing Letters 49(1): 9-14, (1994).. rTFN)setiter_adjappendminpopaddupdate)Gpreorderlowlink scc_found scc_queueiv neighborssourcequeuedonewsccks ڂ/root/GenerationalWealth/GenerationalWealth/venv/lib/python3.13/site-packages/networkx/algorithms/components/strongly_connected.pyrrsvHGII A-./QDO#QI/  "HE%"I$AA"#QK"A( Q$ & !)GJVVAY-'{X[8-0'*gj1I-J -0'*hk1J-K ' IIKzX[0 c'Hr],Chk,Q ) AGGAJ(Hr],Chk,Q"((-! !((+9%0s4F"F  F FF99F6BF.F Fc#n# [[R"URSS9US95n[ U5n[ 5nU(a[ U5U:aUR 5nXT;aM-U1nURU5 U/nU(a[ U5U:axUR 5nURUH=n X;dM URU 5 URU 5 URU 5 M? U(a[ U5U:aMxUv U(a[ U5U:aMgggg7f)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_nodesreverselenr rrrr) rrpostnseenrnewstackrr s r#rrrsd &&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&# UHnSv M g7f)r N).0r!s 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. rz-Connectivity is undefined for the null graph.)r*r'NetworkXPointlessConceptnextrr8s r#rrsGX 1v{)) ?   t1!45 6#a& @@r9T) returns_graphc^^Uc[R"U5n0m0n[R"5nTURS'[ U5S:XaU$[ U5H%umnXBT'TR U4SjU55 M' TS-nUR[U55 URU4SjUR555 [R"X2S5 U$)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. mappingrc3*># UHoT4v M g7fNr3)r4r,rs r#r5condensation.._s1y!1vysr c3X># UHupTUTU:wdMTUTU4v M! g7frAr3)r4urr?s r#r5rBbs6-6TQ'!*PQ :R WQZ Ys**members) r'rDiGraphgraphr* enumerateradd_nodes_fromrangeadd_edges_fromedgesset_node_attributes)rr!rEC componentnumber_of_componentsrr?s @@r#rrs~ {..q1GG A AGGI 1v{!# 9 1y11'q5U/01-.WWY1y1 Hr9rA) __doc__networkxr'networkx.utils.decoratorsr__all__ _dispatchablerrrrrr3r9r#rVs$9 \"^,#^,B\"A#AH\"$>#$>N\"/A#/Ad\"%P &#P r9