wgF%XdZddlZddlmZgdZedej dZedej d dZedej dZ edej d Z edej d d d Z y)zStrongly connected components.N)not_implemented_for)$number_strongly_connected_componentsstrongly_connected_componentsis_strongly_connected&kosaraju_strongly_connected_components condensation undirectedc#Ki}i}t}g}d}|Dcic]}|t||}}|D]"}||vs |g} | s| d}||vr |dz}|||<d} ||D]} | |vs| j| d} n| r||||<||D]?} | |vs|| ||kDrt|||| g||<*t|||| g||<A| j ||||k(r[|h} |r@||d||kDr2|j } | j | |r||d||kDr2|j | | n|j|| r%ycc}ww)aGenerate nodes in strongly connected components of graph. Parameters ---------- G : NetworkX Graph A directed graph. Returns ------- comp : generator of sets A generator of sets of nodes, one for each strongly connected component of G. Raises ------ NetworkXNotImplemented If G is undirected. Examples -------- Generate a sorted list of strongly connected components, largest first. >>> G = nx.cycle_graph(4, create_using=nx.DiGraph()) >>> nx.add_cycle(G, [10, 11, 12]) >>> [ ... len(c) ... for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True) ... ] [4, 3] If you only want the largest component, it's more efficient to use max instead of sort. >>> largest = max(nx.strongly_connected_components(G), key=len) See Also -------- connected_components weakly_connected_components kosaraju_strongly_connected_components Notes ----- Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_. Nonrecursive version of algorithm. References ---------- .. [1] Depth-first search and linear graph algorithms, R. Tarjan SIAM Journal of Computing 1(2):146-160, (1972). .. [2] On finding the strongly connected components in a directed graph. E. Nuutila and E. Soisalon-Soinen Information Processing Letters 49(1): 9-14, (1994).. rTFN)setiterappendminpopaddupdate)Gpreorderlowlink scc_found scc_queueiv neighborssourcequeuedonewsccks v/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/algorithms/components/strongly_connected.pyrrsvHGII A()*1D1J*I*,  "HE"IH$AA"#HQK"1A( Q$  !)!GAJqTLI-'{Xa[8-0'!*gaj1I-J -0'!*hqk1J-K L IIKqzXa[0 c'HYr],Chqk,Q ) AGGAJ(HYr],Chqk,Q"((-! !((+9,+s3EE EE!E$,EBE+)E Ec#>Kttj|jd|}t }|rX|j }||vrtj ||}|Dchc] }||vs| }}|j|||rWyycc}ww)a Generate 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.kosaraju_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.kosaraju_strongly_connected_components(G), key=len) See Also -------- strongly_connected_components Notes ----- Uses Kosaraju's algorithm. F)copy)rN)listnxdfs_postorder_nodesreverser rdfs_preorder_nodesr)rrpostseenrcrnews r"rrrsb &&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=Sq=s )sumrrs r"rrsL =9!<= ==ct|dk(rtjdttt |t|k(S)aWTest directed graph for strong connectivity. A directed graph is strongly connected if and only if every vertex in the graph is reachable from every other vertex. Parameters ---------- G : NetworkX Graph A directed graph. Returns ------- connected : bool True if the graph is strongly connected, False otherwise. Examples -------- >>> 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.)lenr&NetworkXPointlessConceptnextrr5s r"rrsGX 1v{)) ?   t1!45 6#a& @@r6T) 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 ywNr1)r2nrs r"r3zcondensation..Ws1!1v1sr c3PK|]\}}||k7s||fywr?r1)r2urr=s r"r3zcondensation..Zs7%)Q'!*PQ :RWQZ s&&members) r&rDiGraphgraphr8 enumerateradd_nodes_fromrangeadd_edges_fromedgesset_node_attributes)rr rCC componentnumber_of_componentsrr=s @@r"rr s~ {..q1GG A AGGI 1v{!#2 9 1y112q5U/01-.WWY1gy1 Hr6r?) __doc__networkxr&networkx.utils.decoratorsr__all__ _dispatchablerrrrrr1r6r"rTs$9 \"^,#^,B\"9#9x\"$>#$>N\"/A#/Ad\"%P &#P r6