U ?h.@sdZddlZddlmZdddddd gZejed d dZed dd dZed d dZ ed ddZ ed ddZ ed ddd Z dS)zStrongly connected components.N)not_implemented_for$number_strongly_connected_componentsstrongly_connected_componentsis_strongly_connected'strongly_connected_components_recursive&kosaraju_strongly_connected_components condensationZ undirectedc#sni}i}t}g}d}fddD}D]:}||kr,|g}|r,|d} | |krd|d}||| <d} || D]} | |krp|| d} qqp| r@|| || <| D]N} | |kr|| || krt|| || g|| <qt|| || g|| <q||| || kr\| h} |rJ||d|| krJ|} | | q|| | Vq@|| q@q,dS) 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).. rcsi|]}|t|qS)iter.0vGr c/var/www/html/venv/lib/python3.8/site-packages/networkx/algorithms/components/strongly_connected.py Osz1strongly_connected_components..TFN)setappendminpopaddupdate)rZpreorderZlowlinkZ scc_foundZ scc_queueiZ neighborssourcequeuer donewscckr rrrsH;      c#sjttj|jdd|d}t|rf|}|kr6q t||}fdd|D}||Vq dS)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)rcsh|]}|kr|qSr r r seenr r sz9kosaraju_strongly_connected_components..N)listnxZdfs_postorder_nodesreverserrZdfs_preorder_nodesr)rrpostrcnewr r"rrrs0  c#sPfddiiid}gD]}|kr.||EdHq.dS)a!Generate nodes in strongly connected components of graph. Recursive version of algorithm. 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_recursive(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_recursive(G), key=len) To create the induced subgraph of the components use: >>> S = [G.subgraph(c).copy() for c in nx.weakly_connected_components(G)] See Also -------- connected_components Notes ----- Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_. 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).. c3s||<||<|d7}||D]:}|krF||EdH|kr*t|||<q*||krĈ||<|h}d|kr}||<||q||VdS)Nrr)rrrrremove)r cntrZtmpcr componentrootstackvisitvisitedr rr2s$       z6strongly_connected_components_recursive..visitrNr )rr-rr r.rrs?cCstddt|DS)aReturns number of strongly connected components in graph. Parameters ---------- G : NetworkX graph A directed graph. Returns ------- n : integer Number of strongly connected components Raises ------ NetworkXNotImplemented If G is undirected. Examples -------- >>> 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. css|] }dVqdS)rNr )r rr r r /sz7number_strongly_connected_components..)sumrrr r rr s#cCs.t|dkrtdttt|t|kS)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&ZNetworkXPointlessConceptnextrrr r rr2s + cs|dkrt|}ii}t}|jd<t|dkr<|St|D](\}||<fdd|DqDd}|t|| fdd| Dt ||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. Nmappingrc3s|]}|fVqdSNr )r n)rr rr4szcondensation..rc3s2|]*\}}||kr||fVqdSr9r )r ur )r8r rr4smembers) r&rZDiGraphgraphr6 enumeraterZadd_nodes_fromrangeZadd_edges_fromedgesZset_node_attributes)rrr<Cr/Znumber_of_componentsr )rr8rres$>   )N)N) __doc__Znetworkxr&Znetworkx.utils.decoratorsr__all__Z _dispatchrrrrrrr r r rs,   a < \ % 2