fiF%dZddlZddlmZgdZedejdZedejd dZedejdZ edejd Z edejd d d Z dS)zStrongly connected components.N)not_implemented_for)$number_strongly_connected_componentsstrongly_connected_componentsis_strongly_connected&kosaraju_strongly_connected_components condensation undirectedc#HKi}i}t}g}d}fdD}D]v}||vrn|g}|rh|d} | |vr |dz}||| <d} || D]} | |vr|| d} n | r"|| || <| D]Y} | |vrS|| || kr!t|| || g|| <9t|| || g|| <Z||| || krz| h} |r[||d|| krC|} | | |r||d|| kC|| | Vn|| |hxdS)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).. rc<i|]}|t|S)iter).0vGs /var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/networkx/algorithms/components/strongly_connected.py z1strongly_connected_components..Os%***1D1JJ***TFN)setappendminpopaddupdate)rpreorderlowlink scc_found scc_queuei neighborssourcequeuerdonewsccks` rrrs&vHGII A*******I,,  " "HE ,"IH$$AA"#HQK"1A(( Q$),!)!GAJqTLLI--'{Xa[88-0'!*gaj1I-J-J -0'!*hqk1J-K-K IIKKKqzXa[00 c''HYr],Chqk,Q,Q ) AGGAJJJ('HYr],Chqk,Q,Q"((---! !((+++9 ,,,rc#LKttj|d|}t |rY|}|vrtj||}fd|D}||V|WdSdS)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)r"ch|]}|v| Sr r )rrseens r z9kosaraju_strongly_connected_components..s---Qq}}q}}}rN)listnxdfs_postorder_nodesreverserrdfs_preorder_nodesr)rr"postrcnewr+s @rrrrsb &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. c3K|]}dVdS)rNr )rr&s r z7number_strongly_connected_components..s"==Sq======r)sumrrs rrrs+L ==9!<<=== = ==rct|dkrtjdttt |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.NetworkXPointlessConceptnextrr:s rrrsXX 1vv{{) ?    t1!4455 6 6#a&& @@rT) returns_graphc|tj|}ii}tj}|jd<t |dkr|St |D]+\}||<fd|D,dz}|t|| fd| Dtj ||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. Nmappingrc3 K|]}|fV dSNr )rnr s rr8zcondensation..Ws'11!1v111111rrc3bK|])\}}||k||fV*dSrCr )rurrAs rr8zcondensation..ZsP%)Q'!*PQ :R:RWQZ :R:R:R:Rrmembers) r.rDiGraphgraphr< enumerateradd_nodes_fromrangeadd_edges_fromedgesset_node_attributes)rr&rGC componentnumber_of_componentsr rAs @@rrr s&~ {.q11GG A AGI 1vv{{!#22 9 1111y1111111q5U/00111-.WWYY1gy111 HrrC) __doc__networkxr.networkx.utils.decoratorsr__all__ _dispatchablerrrrrr rrrXst$$999999   \""^,^,#"^,B\""999#"9x\""$>$>#"$>N\""/A/A#"/Ad\""%%%P P P &%#"P P P r