h$SrSSKrSSKJr SSKJr SSKJr SSKr SSK J r J r J r SSKJr \ rS /r\ R$S S j5rS rg) z0 Kanevsky all minimum node k cutsets algorithm. N) defaultdict) combinations) itemgetter)build_residual_network edmonds_karpshortest_augmenting_path)!build_auxiliary_node_connectivity all_node_cutsc #: ^^"^## [R"U5(d[R"S5e[R"U5S:Xa SShvN g/n[ U5nUR m"UR Sn[R"UR5n[US5nSUS.nUc[nU[LaSUS 'Uc[R"XS 9n[UR5[S5SS 9SUV V s1sHupU iM n n n [!X 5(aUR#U 5 U v U GHn [%U5U 1- [%X 5- n U GHnU"XEU S 3X^S 340UD6nUR SnX:XdM/UR'SS9VVV s/sHunnoSS:wdMUU4PM sn nn=nnUVV s1sHnUHoiM M sn n=nnUR'SS9VVV s/sH#unnn U SU S:Xd U SS:XdMUUU 4PM% nnnn UR)U5 [R*"U5n[R,"U5nUR Sn[/[05nUR35Hun nUUR#U 5 M UV s1sHn UU iM nn [R4"U5GHPn[%U5R7U5(dM%[%5m#UHnT#R9UU5 M [%5nT#H!n UR9URU 5 M# T#R9U5 X\S 3T#;d X^S 3T#;aM[%5nT#H"mUR9U#U4SjUT55 M$ [;U"4SjU55(aMUVV s1sHunn T"USiM n!nn [=U!5U:XdGM#U U!;dUU!;aGM2U!U;dGM;U!v UR#U!5 GMS UR?X\S 3X^S 3SS9 UR?X^S 3X\S 3SS9 UR?X\S 3X^S 3SS9 UR?X^S 3X\S 3SS9 UR?X^S 3X\S 3SS9 UR?X\S 3X^S 3SS9 URAU5 GM GM gGNs sn n fs sn nnfs sn nfs sn nnfs sn fs sn nf7f)aReturns all minimum k cutsets of an undirected graph G. This implementation is based on Kanevsky's algorithm [1]_ for finding all minimum-size node cut-sets of an undirected graph G; ie the set (or sets) of nodes of cardinality equal to the node connectivity of G. Thus if removed, would break G into two or more connected components. Parameters ---------- G : NetworkX graph Undirected graph k : Integer Node connectivity of the input graph. If k is None, then it is computed. Default value: None. flow_func : function Function to perform the underlying flow computations. Default value is :func:`~networkx.algorithms.flow.edmonds_karp`. This function performs better in sparse graphs with right tailed degree distributions. :func:`~networkx.algorithms.flow.shortest_augmenting_path` will perform better in denser graphs. Returns ------- cuts : a generator of node cutsets Each node cutset has cardinality equal to the node connectivity of the input graph. Examples -------- >>> # A two-dimensional grid graph has 4 cutsets of cardinality 2 >>> G = nx.grid_2d_graph(5, 5) >>> cutsets = list(nx.all_node_cuts(G)) >>> len(cutsets) 4 >>> all(2 == len(cutset) for cutset in cutsets) True >>> nx.node_connectivity(G) 2 Notes ----- This implementation is based on the sequential algorithm for finding all minimum-size separating vertex sets in a graph [1]_. The main idea is to compute minimum cuts using local maximum flow computations among a set of nodes of highest degree and all other non-adjacent nodes in the Graph. Once we find a minimum cut, we add an edge between the high degree node and the target node of the local maximum flow computation to make sure that we will not find that minimum cut again. See also -------- node_connectivity edmonds_karp shortest_augmenting_path References ---------- .. [1] Kanevsky, A. (1993). Finding all minimum-size separating vertex sets in a graph. Networks 23(6), 533--541. http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract zInput graph is disconnected.r Nmappingcapacity)rresidualT two_phase) flow_func)keyreverseBA flow_value)dataflowrc3:># UHoT;dM TU4v M g7f)Nr ).0wSus [/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/connectivity/kcutsets.py all_node_cuts..s%W6HUVJfq!f6Hs  c3J># UHupTUSTUS:gv M g7f)idNr )rrrH_nodess rr r!s*SFDA71:d+wqz$/??Fs #r#)r)!nx is_connected NetworkXErrordensityr nodesgraphcopy_predrdefault_flow_funcrnode_connectivitysorteddegreer_is_separating_setappendsetedgesremove_edges_fromtransitive_closure condensationrlistitems antichainsissubsetupdateanylenadd_edgeadd_edges_from)$GkrseenHroriginal_H_predRkwargsndXx non_adjacentvrrrE1 flowed_edgesedgeVE1incident_nodessaturated_edges R_closureLcmapinv_cmapscc antichain S_ancestorscutset_node_cutr$rs$ ` @@rr r sF ??1  =>>  zz!}  D *!,AggGggi Gii(Oq*-A$! 4F% ,,"{ y   8ahhjjmTJ2ANONtqNAO! A 1v|c!$i/ A! |1-'*Q/?J6JA.J-.GGG,>%,>y1aF)q.FQF,>%\79'Gbd$Q$b'GGn &'WW$W%7#%7 Aq}& 1Qz]a5GQ1I%7 # ##O411!4 OOA&wwy)&t,"jjlFAsSM((++),,1tAw,"$q!1Iy>22377 A(#/ )"%%K#**9??1+=>HH[)!*Q'q0wzl!4D4I  UF %Woa6H%WWSFSSS =CDVTQ 4 0VHD8})=AM$#4/"*N KK1I"2Z gj\+ |1-= J gj\+ |1-= J gj\+ |1-= J gj\+ |1-= J gj\+ |1-= J gj\+ |1-= J  1q C 6 P$%(H#-> EsATS3B4T S6A8TT(S< <S<  TT %T>T  T (BT9TDTT .TTCT6%Tc[U5[U5S- :Xag[R"X/5n[R"U5(agg)z)Assumes that the input graph is connectedr TF)r>r%restricted_viewr&)rAcutrDs rr1r1s@ 3x3q6A: 12&A q )NN)__doc__r+ collectionsr itertoolsroperatorrnetworkxr%networkx.algorithms.flowrrrutilsr r-__all__ _dispatchabler r1r rarrks\ #" 5   F2F2Rra