ܛ7i&XdZddlZddlmZgdZedej dZedej d dZedej dZ edej d Z edej d d d Z y)zStrongly connected components.N)not_implemented_for)$number_strongly_connected_componentsstrongly_connected_componentsis_strongly_connected&kosaraju_strongly_connected_components condensation undirectedc#Ki}i}t}g}d}|Dcic]}|t|j|}}|D],}||vs |g} | s| d}||vr |dz}|||<d} ||D]} | |vs| j| d} n| r||||<|j|D]?} | |vs|| ||kDrt |||| g||<*t |||| g||<A| j ||||k(r[|h} |r@||d||kDr2|j } | j | |r||d||kDr2|j| | n|j|| r/ycc}ww)aGenerate nodes in strongly connected components of graph. Parameters ---------- G : NetworkX Graph A directed graph. Returns ------- comp : generator of sets A generator of sets of nodes, one for each strongly connected component of G. Raises ------ NetworkXNotImplemented If G is undirected. Examples -------- Generate a sorted list of strongly connected components, largest first. >>> G = nx.cycle_graph(4, create_using=nx.DiGraph()) >>> nx.add_cycle(G, [10, 11, 12]) >>> [ ... len(c) ... for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True) ... ] [4, 3] If you only want the largest component, it's more efficient to use max instead of sort. >>> largest = max(nx.strongly_connected_components(G), key=len) See Also -------- connected_components weakly_connected_components kosaraju_strongly_connected_components Notes ----- Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_. Nonrecursive version of algorithm. References ---------- .. [1] Depth-first search and linear graph algorithms, R. Tarjan SIAM Journal of Computing 1(2):146-160, (1972). .. [2] On finding the strongly connected components in a directed graph. E. Nuutila and E. Soisalon-Soinen Information Processing Letters 49(1): 9-14, (1994).. rTFN)setiter_adjappendminpopaddupdate)Gpreorderlowlink scc_found scc_queueiv neighborssourcequeuedonewsccks n/home/rose/Desktop/poly/venv/lib/python3.12/site-packages/networkx/algorithms/components/strongly_connected.pyrrsvHGII A-./QDO#QI/  "HE"IH$AA"#HQK"1A( Q$ & !)!GAJVVAYI-'{Xa[8-0'!*gaj1I-J -0'!*hqk1J-K ' IIKqzXa[0 c'HYr],Chqk,Q ) AGGAJ(HYr],Chqk,Q"((-! !((+90s4E3 E. E3E3 !E3.6E3%BE3?)E3* E3c#8Kttj|jd|}t |}t }|rt ||kr|j }||vr%|h}|j||g}|r{t ||krm|j }|j|D]:} | |vs|j| |j| |j| <|rt ||krm||rt ||kryyyyw)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 K|]}dyw)r N).0r!s r# z7number_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'NetworkXPointlessConceptnextrr7s r#rrsGX 1v{)) ?   t1!45 6#a& @@r8T) returns_graphc|tj|}ii}tj}|jd<t |dk(r|St |D]$\}||<j fd|D&dz}|jt||jfd|jDtj||d|S)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&K|]}|f ywNr3)r4r,rs r#r5zcondensation.._s1y!1vysr c3PK|]\}}||k7s||fywr@r3)r4urr>s r#r5zcondensation..bs6-6TQ'!*PQ :RWQZ Ys&&members) r'rDiGraphgraphr* enumerateradd_nodes_fromrangeadd_edges_fromedgesset_node_attributes)rr!rCC componentnumber_of_componentsrr>s @@r#rrs~ {..q1GG A AGGI 1v{!# 9 1y11'q5U/01-.WWY1gy1 Hr8r@) __doc__networkxr'networkx.utils.decoratorsr__all__ _dispatchablerrrrrr3r8r#rTs$9 \"^,#^,B\"A#AH\"$>#$>N\"/A#/Ad\"%P &#P r8