+ j$Rt^RIt^RIt^RIt.ROt]P !R.RO4t]P !R.RO4t]P!R^R^/RR/R7R R l4t ]P!R^R^/RR/R7R R l4t ]P!R^R^/RR/R7R R l4t ]P!R^R^/RR/R7R R l4t ]P!R^R^/RR/R7R R l4t]P!R^R^/RR/R7R Rl4t]P!R^R^/RR/R7R Rl4t]P!R^R^/RR/R7R Rl4t]P!R^R^/RR/R7R Rl4tRtRtRtRtRtRtRtRtRtRtRtR#)!u *************** VF2++ Algorithm *************** An implementation of the VF2++ algorithm [1]_ for Graph Isomorphism testing. The simplest interface to use this module is to call: `vf2pp_is_isomorphic`: check whether two graphs are isomorphic. `vf2pp_isomorphism`: obtain the node isomorphism mapping between two graphs, if they are isomorphic. `vf2pp_all_isomorphisms`: generate all possible isomorphism mappings between two graphs, if isomorphic. `vf2pp_subgraph_is_isomorphic`: check whether a specified graph is isomorphic to an induced subgraph of the other graph. `vf2pp_subgraph_isomorphism`: obtain the node isomorphism mapping between a specified graph and any induced subgraph of the other graph, if possible. `vf2pp_all_subgraph_isomorphisms`: generate all possible isomorphism mappings between the full graph and the specified induced subgraph. `vf2pp_is_monomorphic`: check whether two graphs are monomorphic. That is, the node and edge sets of the subgraph are subsets of the full graph's node and edge sets. `vf2pp_monomorphism`: obtain the node monomorphism mapping from the full graph to the specified subgraph if possible. `vf2pp_all_monomorphisms`: generate all possible monomorphism mappings between the graph and the specified subgraph. Introduction ------------ The VF2++ algorithm, follows a similar logic to that of VF2, while also introducing new easy-to-check cutting rules and determining the optimal access order of nodes. It is also implemented in a non-recursive manner, which saves both time and space, when compared to its previous counterpart. An improved node ordering is obtained after taking into consideration both the degree and the label rarity of each node. This way we consider the nodes that eliminate the most branches of the possible mapping search tree, so we can cut out unfruitful branches early in the process. Warning: The VF2++ paper uses the symbols ``G1`` and ``G2`` for the two graphs of interest just as the VF2 paper does. But for subgraph functions the first graph is smaller in VF2++ while the second is smaller for VF2 and for ISMAGS. This implementation, VF2pp, matches the VF2 and ISMAGS notation with the second input being no larger than the first. To avoid confusion with the papers we name the graphs ``FG`` and ``SG`` for full graph and smaller graph. For VF2pp, ``SG`` corresponds to the paper's ``G1`` while ``FG`` corresponds to ``G2``. This does not matter for the isomorphism functions (where the graphs have the same size). Examples -------- Suppose SG and FG are Isomorphic Graphs. Verification is as follows: Without node labels: >>> import networkx as nx >>> SG = nx.path_graph(4) >>> FG = nx.path_graph(4) >>> nx.vf2pp_is_isomorphic(FG, SG, node_label=None) True >>> map = nx.vf2pp_isomorphism(FG, SG, node_label=None) >>> map == {1: 1, 2: 2, 0: 0, 3: 3} True With node labels: >>> nx.set_node_attributes(SG, dict(zip(SG, ["blue", "red", "cyan", "pink"])), "label") >>> nx.set_node_attributes(FG, dict(zip(FG, ["blue", "red", "cyan", "pink"])), "label") >>> nx.vf2pp_is_isomorphic(FG, SG, node_label="label") True >>> map = nx.vf2pp_isomorphism(FG, SG, node_label="label") >>> map == {1: 1, 2: 2, 0: 0, 3: 3} True For subgraph isomorphism we look for induced subgraphs of FG that are isomorphic to SG. The process is similar to graph isomorphism with a different function: >>> SG = nx.path_graph(3) >>> FG = nx.path_graph(4) >>> nx.vf2pp_subgraph_is_isomorphic(FG, SG, node_label=None) True >>> map = nx.vf2pp_subgraph_isomorphism(FG, SG, node_label=None) >>> map == {1: 1, 2: 2, 0: 0} True With node labels: >>> nx.set_node_attributes(SG, dict(zip(SG, ["blue", "red", "cyan"])), "label") >>> nx.set_node_attributes(FG, dict(zip(FG, ["blue", "red", "cyan", "pink"])), "label") >>> nx.vf2pp_subgraph_is_isomorphic(FG, SG, node_label="label") True >>> map = nx.vf2pp_subgraph_isomorphism(FG, SG, node_label="label") >>> map == {1: 1, 2: 2, 0: 0} True For subgraph monomorphism we look for possibly non-induced subgraphs of FG that are isomorphic to SG. That means we only need a subset of nodes and edges of the first that map to nodes and edges of the second. But not all edges in the second graph need to be mapped to, even if that edge involves two nodes that are mapped to. A classic example of this is a path graph mapping to a subgraph of a cycle graph with the same number of nodes. The missing edge in the path graph means that no subgraph isomorphism exists. But a monomorphism exists because not all induced edges need to be mapped to. >>> SG = nx.path_graph(4) >>> FG = nx.cycle_graph(4) >>> nx.vf2pp_is_monomorphic(FG, SG, node_label=None) True >>> map = nx.vf2pp_monomorphism(FG, SG, node_label=None) >>> map == {1: 2, 2: 3, 0: 1, 3: 0} True With node labels: >>> nx.set_node_attributes(SG, dict(zip(SG, ["blue", "red", "cyan", "pink"])), "label") >>> nx.set_node_attributes(FG, dict(zip(FG, ["blue", "red", "cyan", "pink"])), "label") >>> nx.vf2pp_is_monomorphic(FG, SG, node_label="label") True >>> map = nx.vf2pp_monomorphism(FG, SG, node_label="label") >>> map == {1: 1, 2: 2, 0: 0, 3: 3} True References ---------- .. [1] Jüttner, Alpár & Madarasi, Péter. (2018). "VF2++—An improved subgraph isomorphism algorithm". Discrete Applied Mathematics. 242. https://doi.org/10.1016/j.dam.2018.02.018 N _GraphInfoSGFG _StateInfo node_label default_label)graphs node_attrsc Z\\WW#RR74pV# \dR#i;i)aReturn an isomorphic mapping between `FG` and `SG` if it exists. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Returns ------- dict or None Node mapping if the two graphs are isomorphic. None otherwise. ISOPTNnext_all_morphisms StopIterationrrrrmappings&&&& f/home/luca/screen-checking/.venv/lib/python3.14/site-packages/networkx/algorithms/isomorphism/vf2pp.pyvf2pp_isomorphismrs10~bjERS   **c Z\\WW#RR74R# \dR#i;i)Examines whether SG and FG are isomorphic. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Returns ------- bool True if the two graphs are isomorphic, False otherwise. r r TFrrrrrs&&&&rvf2pp_is_isomorphicr-0 ^BJ% HI   **c#>"\WW#RR7RjxL R#L5i)aYields all the possible mappings between FG and SG. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Yields ------ dict Isomorphic mapping between the nodes in `FG` and `SG`. r r Nrrs&&&&rvf2pp_all_isomorphismsr0bjEJJJ c Z\\WW#RR74pV# \dR#i;i)aReturn an isomorphic mapping between nodes of `FG` and `SG` if it exists. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Returns ------- dict or None Isomorphism mapping nodes of one graph to nodes of the other. If not subgraph isomorphic, return None. INDr Nrrs&&&& rvf2pp_subgraph_isomorphismr$s12~bjERS rc Z\\WW#RR74R# \dR#i;i)rr#r TFrrs&&&&rvf2pp_subgraph_is_isomorphicr&1rrc#>"\WW#RR7RjxL R#L5i)aYields all the possible subgraph isomorphisms between FG and SG. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for subgraph isomorphisms. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Yields ------ dict Subgraph isomorphisms mapping the nodes in `SG` to nodes in `FG`. r#r Nrrs&&&&rvf2pp_all_subgraph_isomorphismsr(Pr r!c Z\\WW#RR74pV# \dR#i;i)aReturn a monomorphic mapping between `FG` and `SG` if it exists. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for monomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Returns ------- dict or None Node mapping if the two graphs are isomorphic. None otherwise. MONOr Nrrs&&&& rvf2pp_monomorphismr+ks10~bjFST rc Z\\WW#RR74R# \dR#i;i)aExamines whether SG and FG are monomorphic. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for monomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Returns ------- bool True if the two graphs are monomorphic, False otherwise. r*r TFrrs&&&&rvf2pp_is_monomorphicr-s-0 ^BJ& IJ rc#>"\WW#RR7RjxL R#L5i)aYields all the possible monomorphisms between nodes of FG and SG. A monomorphism is an injective version of an isomorphism. If two nodes in SG are connected by an edge, the pre-image nodes in FG must also be connected. But two mapped nodes connected by an edge in FG may not have an edge in SG. Maintaining both edges and non-edges (an induced subgraph) is provided by subgraph isomorphism functions. Parameters ---------- FG, SG : NetworkX Graph or MultiGraph instances. The two graphs to check for isomorphism. node_label : str, optional The name of the node attribute to be used when comparing nodes. The default is ``None``, meaning node attributes are not considered in the comparison. Any node that doesn't have the `node_label` attribute uses `default_label` instead. default_label : scalar Default value to use when a node doesn't have an attribute named `node_label`. Default is ``None``. Yields ------ dict Isomorphic mapping of the nodes in `FG` to nodes in `SG`. r*r Nrrs&&&&rvf2pp_all_monomorphismsr/s<bjFKKKr!c #a!a""\V4\V4reV^8XgV^8XdR#VP4pWpP48wd\P!R4hV'd\p\ p M \ p\p \WW#V4wrV w o"rpp o!S"!WV4'gR#\PPV 4p\;QJd.V!V"3RlVP44F 'gK RM# RM!V!V"3RlVP444pT'dR#\T 4p\T4UUu/uF wppTTbK pppT^,pY3pT\!T!T.TO5!43.pT P"pT P$p^pT'dTR,wpp\'T4p\-TTY4'gK5\T4TP/4^, 8XdTP14pTTT&TxKuTTT&TTT&\3TTY4T^, pTT,pT!T.TO5!p TP5T\!T 434KR# \dR#i;iuuppi \(dYV, T\T4, 8d/T^, pTT,pT\!T!T.TO5!43TR&EK6TP+4T'dSTR,^,pTT,pTT,pTP+T4TP+T4T !TTY4EKR#i;i5i)Fz)SG and FG must have the same directednessc3<"TFVwrS\P8H;'dVS9;'g(S!\V4\SV,44'*xKX R#5iN)operatoreqlen).0labelnodes FG_by_labelSG_fitss& r !_all_morphisms..s_ !4  # @ @[(@ @ @3u:s;u+='>?? @ 3s A! A!0A!TN)r6 is_directednx NetworkXError_find_candidates_Di_restore_Tinout_Di_find_candidates_restore_Tinout _init_infoutilsgroupsanyitemsKeyError_matching_order enumerateiterrrev_maprrpop _feasibilitynumber_of_nodescopy_update_Tinoutappend)#rrrrr N1N2directedfind_candidatesrestore_Tinout graph_info state_info_ SG_labels FG_labels SG_by_labellabels_mismatch node_orderinode order_index start_nodeargsstackrrO node_number current_nodecandidate_iter candidatecand cp_rev_maptmpr:r;s#&&&&& @@rrrs Wc"g Qw"'~~H>>##JKK-+*(( 2NJCM@GQ1aIq![ 2??((//),K# !, 1 1 3 ### !, 1 1 3  !,J*3J*?@*?wq$47*?K@AJ  #D$zADAB C DE  G  GK ',Ry$ n ^,I,  i H H7|r113a77$\\^ (4 9%  %.GL !!-GI  <J K 1 Kk*D!$..C LL$S * + W ) A$ ws7|33q !+.!4(Dt(D#EFb  IIKRy|)$/ t} D! D!tT:B ' sA'M,A#M I!#I!'I!(M0M I3AM! M. I99MBM! I0,M/I00 M9AL= ML='AL=5M<L==Mc VR8Xd\PM\PpVR8wd\PM\PpVP4p\ VP W#R74p\ VP W#R74p \ PPV 4p V'd~\VPVP4U U U Uu/uFwwrwrWV3bK pp p p p\VPVP4U U U Uu/uFwwrwrWV3bK pp p p pM*\ VP4p\ VP4p\VVVVVVV VVV 4 p//pp\4\4pp\4\4pp\VP 44p\VP 44p\VVVVVVVV4pVV3#uupp p p iuupp p p i)r r*)datadefault)r4r5ler?dictr9r@rGrHzip in_degree out_degreedegreersetr)rrrrr r; MONO_fitsrXr^r_r:nrcr]o SG_degree FG_degreer[r rev_mappingT1T1_inT2T2_inT1_tildeT2_tilder\s&&&&& rrFrF7s5[hkkhkkG!V| I~~HRXX:XEFIRXX:XEFI((//),K58r}}5UV5U>6A6AQAY5U V58r}}5UV5U>6A6AQAY5U V O O    Jr[GsuBsuB288:H288:Hb%2uhJ z !!;WVs !G+ G3 c aaaaVw rpoorV'dSPRR7o\SP44pVP4UUu/uFwrgV\ V4bK uppoSUu/uFq^bK upo.p V'Ed\ VV3RlV44p VU u.uFp SSV ,,V 8XgKV NK p p \ V SPPR7p \P!SV 4EF"pVP4pV'gK\ V3RlV44pVU u.uFp SV ,V8XgKV NK pp \ V3RlV44pVU u.uFp SPV ,V8XgKV NK! pp \ VVV3RlR7pV PV4SPV4FpSV;;,^, uu&K VPV4SSV,;;,^,uu&VPV4EK EKV #uuppiuupiuup iuup iuup i)aThe node ordering as introduced in VF2++. Notes ----- Taking into account the structure of the Graph and the node labeling, the nodes are placed in an order such that, most of the unfruitful/infeasible branches of the search space can be pruned on high levels, significantly decreasing the number of visited states. The premise is that, the algorithm will be able to recognize inconsistencies early, proceeding to go deep into the search tree only if it's needed. Returns ------- node_order: list The ordering of the nodes. T)as_viewc3D<"TFpSSV,,xK R#5ir3)r7xr^ label_raritys& rr<"_matching_order..sJ\il33\s )keyc36<"TFpSV,xK R#5ir3r)r7r{ used_degreess& rr<rs%L|!l1oo|sc3J<"TFpSPV,xK R#5ir3)rx)r7r{rs& rr<rs M7L!17Ls #c$<SSV,,#r3r)rr^rs&r!_matching_order..sL14N) to_undirectedryr9rJr6minmaxrx __getitem__r@ bfs_layersrSrU neighborsremovediscard)r[r]rXrnodes_of_FGLabels V1_unorderedr8r9rdrb max_rarityr{ rarest_nodesmax_node dlevel_nodes nodes_to_addmax_used_degreemax_used_degree_nodes max_degreemax_degree_nodes next_noderr^rrs& @@@@rrLrLcs"EOAAqBIq!Q   d  +rxxz?L:K:Q:Q:ST:S,%E3u:%:STL(*+!G+LJ ,J\JJ # #!|IaL'AZ'OAA|  |)>)>?MM"h7L',,.L,"%%L|%L"L+)+!|A//QAA|&)! M7L MM 4$4! ! 8RAA4!$ $*N !!),LL3D &!+&4##I.Yy12a72$$Y/+8. EU+  )$s0H05 H6(H;H;;II1IIc Vw r4rVrxrYrVwrr^W,W,VPW4pppWp,Uu.uFpVV 9gK VNK ppV'dV^,pVPV V,,P4W,,pVV P4,pVR,F,pVPVPV V,,4K. VUu0uF>pV!VVPVV44'gK$V!VV V,4'gK<VkK@ ppV'gV\P 8XdV#W,Uu0uFpV!VV V,4'gKVkK ppV\P 8XdVPV4MVP V 4VUu0uF&pV!VVPVV44'gK$VkK( ppV#uupiuupiuupiuupi)z6Given node u of SG, finds the candidates of u from FG.NN)number_of_edges_adjkeysintersection_updater4r5difference_update)ur[r\r;rzr]rrSG_lblsSG_degFG_degr:rrOru_labelu_degu_loopsnbr covered_nbrscandsr{resultvs&&& rrDrDsNXJGrAv0:-GaAq!%j&)R5G5G5MGUG#%5;5CC7NCC5L;1o %**,{/CC ##C  % %bgggcl&; <$  ""4"4Q":; ufQi( A   Y(++-M$, J,1vay0IQQ,E JHKK !!(+ ( OA)GR5G5G15M"NaaF O M7<  K Ps5 G- G--!G2G2+G2G79G7=!G<#G<c aVw or4rVrtrp VwrrMWp,W,VPW4prW`,Uu.uFpVV 9gK VNK ppVPV,Uu.uFpVV 9gK VNK ppV'g V'EdV'dV^,pVPV V,,P4V P4, pVR,F,pVP VPV V,,4K. MDVP 4p\ VPV V,,4pVPV 4VF,pVP VPV V,,4K. VP W,4VUu0uFpV!VVPVV44'gK$\;QJd/V3Rl\WV,44F 'dK RM$ RM !V3Rl\WV,444'gKVkK ppV'gV\P8XdV#\ W,4pV\P8XdVP V 4MVPV 4VUu0uFpV!VVPVV44'gK$\;QJd/V3Rl\WV,44F 'dK RM$ RM !V3Rl\WV,444'gKVkK ppV#uupiuupiuupiuupi)r1rc38<"TFwrS!W4xK R#5ir3r)r7udvdr;s& rr<&_find_candidates_Di..sG1Fvr72??1FsFTc30<"TF pS!V!xK R#5ir3r)r7dsr;s& rr<rs<&;w|&;s) rpred_predrrrPryrrallrur4r5)rr[r\rzr]rrrrrr:rrOrrrrsucccovered_successorsrcovered_predecessorsrrrr{r;s&&& @rrBrBsMWJGY27v{0:-GaAq!%j&)R5G5G5MGU+-5D54DGO$$5D-/WWQZKZT47?DDZK11 %a(DHHWT]+002W\\^CE*2..))"((74=*AB/(++-D ./E  # #G ,(D  % %bgggdm&< =) !!+"67 ""4"4Q":; sGU1I1FGsssGU1I1FGG A   Y(++-M  $ %EHKK !!(+ (A Wb00A6 7  3.+!H%Q 2 21a 8 8%"T)reversec3H<"TFpSPSV4xK R#5ir3rr7rrrs& rr<r,rrc3B<"TFwrS!W4'*xK R#5ir3rr7ucvcr;s& rr<r-K9Jvr72?**9Jc3H<"TFpSPSV4xK R#5ir3rrs& rr<r?rrc3H<"TFpSPSV4xK R#5ir3rrs& rr<r@rrc3B<"TFwrS!W4'*xK R#5ir3rrs& rr<rArr) is_multigraphrr@rGrHrrrJsortedrIrur6r4rs)#rrr[r\rzrXr^r_r]rrrrrr multigraphunbrsvnbrsru_labels_successorsv_labels_successorsupredsvpredsn1u_labels_predecessorsn2v_labels_predecessorsr8ucntsvcntsupredvpredrrr;s#ff&& @@@rrrsJTGGY"b)1a5?2Aqer(!!#99r'7'7'9J771:rwwqz5E((//%*P%33 #+>%*PQ((//%*P%33 #+>%*PQ &++-/B/G/G/I J J!bhhqk "V0TVrYr]1BV0T U "V0TVrYr]1BV0T U,1135J5O5O5QRR/557LE5'.EH%HRVWH%HRVW3KUE9JK333KUE9JKKK 3rEz?CU O<<EEM(:C .Vs!F1g&wqz&$$TFc3L<"TFqS9gK SV,S9xK R#5ir3r)r7r{rOrs& rr<rYs!JEq'\*71:U*Erc3L<"TFqS9gK SV,S9xK R#5ir3r)r7r{rrs& rr<r_s!HA<'wqz'rc3L<"TFqS9gK SV,S9xK R#5ir3r)r7r{rOrs& rr<rbs!LVG|+71:V+Vrc 3p<"TF+qS9gK S!S!SV4S!SSV,44xK- R#5ir3rr7r{FGneMONO_opSGnerrrs& rr<rhs6 >CG| 4GDAJQ 3 4 4e6&6c3p<"TF+qS9gK S!S!SSV,4S!SV44xK- R#5ir3r)r7r{rrrrOrrs& rr<rms7BGQPW<8Q +T!QZ88%rc3p<"TF+qS9gK S!S!VS4S!SV,S44xK- R#5ir3rrs& rr<rus6 >DW 4GDAJWQZ 3 4 4frc3h<"TF'qS9gK S!SV,S4S!VS48gxK) R#5ir3r)r7r{rrrOrrs& rr<rzs.UfW 44 A&$q!*4fs2"2) rrOrrrrIr4r5rr)rrr[r\r]rXrrrrrrrrOrrrrsff&& @@@@@@@@@rrrMsV'1$Awb!)):+=+=GW!!#99r'7'7'9J771:rwwqzLE5!bhhqk : 3FF333FF F F hkk !sJEJsssJEJJJ 3HH333HH H H hkk !sLVLsssLVLLL'');); ds  >C sss  >C    hkk !3BG333BGs  >D sss  >D    hkk !sUUfUsssUUfUUUrcVvrErgpVwrrrrWp,Uu0uFpVV9gK VkK ppWa,Uu0uFpVV 9gK VkK ppV PV4V PV4V PV4V PV4V PV4VPV4V PV4VPV4V'gR#VPV,Uu0uFpVV9gK VkK ppVPV,Uu0uFpVV 9gK VkK ppV PV4VPV4V PV4VPV4V PV4VPV4V PV4VPV4R#uupiuupiuupiuupi)aUpdates the Ti/Ti_out (i=1,2) when a new node pair u-v is added to the mapping. Notes ----- This function should be called right after the feasibility checks are passed, and node1 is mapped to node2. The purpose of this function is to avoid brute force computing of Ti/Ti_out by iterating over all nodes of the graph and checking which nodes satisfy the necessary conditions. Instead, in every step of the algorithm we focus exclusively on the two nodes that are being added to the mapping, incrementally updating Ti/Ti_out. N)updaterrr) new_node1 new_node2r[r\r]rXrrrrrrrrrrsuncovered_successors_SGuncovered_successors_FGpuncovered_preds_SGuncovered_preds_FGs&&&& rrTrTs",AqBQEOBG"X5*,-L-Q1G;Kqq-L*,-P-Q1K;Oqq-PII%&II%&JJyJJy 67 67 Y Y %'WWY%7L%71G;K!!%7L%'WWY%7P%71K;O!!%7P LL#$ LL#$ MM) MM) 12 12 Y Y9MP MPs- GG GG5 G G  G.GcaaVvrErgpVwoorrrRpWp,FpVS9dRpVPV4K\;QJd%V3RlW,4F 'gK RM RM!V3RlW,44'dKmVPV4V PV4K V'gV PV4RpWa,FpVS9dRpV PV4K\;QJd%V3RlWo,4F 'gK RM RM!V3RlWo,44'dKmV PV4V PV4K V'gV PV4R#R#)zYRestores the previous version of Ti/Ti_out when a node pair is deleted from the mapping. 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