+ )i7Rt^RIHt^RIHtHt^RIt^RIH t H t .ROt Rt Rt ]!] 4UUu/uFwrV] V^, ,bK upptRt] !R4]P"RRl44t]P"R4t] !R4]P"!R R 7R 44t] !R4]P"R 44t] !R4]P"R 44tR#uuppi)z*Functions for analyzing triads of a graph.) defaultdict) combinations permutationsN)not_implemented_forpy_random_statecVaW^3W!^3W^3W1^3W#^3W2^ 33p\V3RlV44#)zReturns the integer code of the given triad. This is some fancy magic that comes from Batagelj and Mrvar's paper. It treats each edge joining a pair of `v`, `u`, and `w` as a bit in the binary representation of an integer. c3L<"TFwrq2SV,9gKVxK R#5iN).0uvxGs& X/var/www/html/photoedit/myenv/lib/python3.14/site-packages/networkx/algorithms/triads.py _tricode..~s4WQ1qt)qqs$ $)sum)rr r wcombossf&&& r_tricoderus@Qi!Q1Iay1*qRj QF 44 44 undirectedc  aa a!a"\VPV44o!Ve%\V4\S!48wd \R4h\V4oS\S!4, p\ S!4UUu/uFwr4WCbK pppV'd8VP S!, pVP V3Rl\ V444VUu/uFJqDVPV,P4VPV,P4,bKL ppVUu/uFJqDVPV,P4VPV,P4,bKL upo V'dXUu/uFJqDVPV,P4VPV,P4, bKL upo"\V!V"3RlV44pV^,p \V V!3RlV44p V ^,p \U u/uFq^bK p p S!EFJpW~,pS V,pV'd ^;p;p;ppVEFpVV,W^,8:dKVV,pVV,VV0, pVF}pVV,VV,8g9W^,VV,u;8dVV,8gK=MKAWV,9gKP\WVV4pV \V,;;,^, uu&K VV9d.V R;;,S\V4, ^, , uu&M,V R;;,S\V4, ^, , uu&V'gEK#VS!9gEK-S"V,pX\VVS!, ,4, pX\VV, S!, 4, pS V,pX\VVS!, ,4, pX\VV, S!, 4, pEK V'gEKV R;;,X XX^,,, , uu&V R;;,X XX^,,, , uu&EKM SS^, ,S^, ,^,pW"^, ,V^, ,^,pVV, pV\V P44, V R&V #uuppiuupiuupiuupiuup i)aDetermines the triadic census of a directed graph. The triadic census is a count of how many of the 16 possible types of triads are present in a directed graph. If a list of nodes is passed, then only those triads are taken into account which have elements of nodelist in them. Parameters ---------- G : digraph A NetworkX DiGraph nodelist : list List of nodes for which you want to calculate triadic census Returns ------- census : dict Dictionary with triad type as keys and number of occurrences as values. Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1), (3, 4), (4, 1), (4, 2)]) >>> triadic_census = nx.triadic_census(G) >>> for key, value in triadic_census.items(): ... print(f"{key}: {value}") 003: 0 012: 0 102: 0 021D: 0 021U: 0 021C: 0 111D: 0 111U: 0 030T: 2 030C: 2 201: 0 120D: 0 120U: 0 120C: 0 210: 0 300: 0 Notes ----- This algorithm has complexity $O(m)$ where $m$ is the number of edges in the graph. For undirected graphs, the triadic census can be computed by first converting the graph into a directed graph using the ``G.to_directed()`` method. After this conversion, only the triad types 003, 102, 201 and 300 will be present in the undirected scenario. Raises ------ ValueError If `nodelist` contains duplicate nodes or nodes not in `G`. If you want to ignore this you can preprocess with `set(nodelist) & G.nodes` See also -------- triad_graph References ---------- .. [1] Vladimir Batagelj and Andrej Mrvar, A subquadratic triad census algorithm for large sparse networks with small maximum degree, University of Ljubljana, http://vlado.fmf.uni-lj.si/pub/networks/doc/triads/triads.pdf z3nodelist includes duplicate nodes or nodes not in Gc3<<"TFwrW!S,3xK R#5ir r )r inNs& rr!triadic_census..s?(>!U(>sc3X<"TFpSV,Fq"S9gK ^xK K! R#5iNr )r rnbrnodesetsgl_nbrss& rrr&V[HQKKSgCU!!K![**c3X<"TFpSV,Fq"S9gK ^xK K! R#5ir r )r rr"dbl_nbrsr#s& rrrr%r&102012003)set nbunch_iterlen ValueError enumeratenodesupdatepredkeyssuccr TRIAD_NAMESrTRICODE_TO_NAMEvalues)#rnodelistNnotrrm not_nodesetnbrssglsgl_edges_outsidedbldbl_edges_outsidenamecensusr vnbrs dbl_vnbrs sgl_unbrs_bdy sgl_unbrs_out dbl_unbrs_bdy dbl_unbrs_outr unbrs neighborsrcode sgl_unbrs dbl_unbrstotal_trianglestriangles_without_nodeset total_censusrr(r#r$s#&& @@@@rtriadic_censusrRsP!--)*GH W =NOO AA s7| D$G,-,$!,A- gg'  ? +(>?? => >Aqqvvay~~!&&).."22 2AD >@AB1166!9>>#affQinn&666BH DOPKqqvvay~~'!&&)..*:::KPV[VV1HV[VV1H#. .+$Ag+F . QK LM MM MM MMMAtqt|GE1a&0IQ4!A$;14!A$#51#5#5!7:J#A!Q/D?401Q61 I~u S^!3a!77 u S^!3a!77 t($QK Y%@!AA Y%6%@!AA $QK Y%@!AA Y%6%@!AA 58 4 5M.--STBT2TU UM 5M.--STBT2TU UMKRAE{a!e,2O!%!2dQh!?A E"%>>L 3v}}#77F5M MK . ?BQ/s!2 S(AS.AS3:AS8 S=cfa\S\P4'dSP4^8Xd{\P!S4'd_\ ;QJd-V3RlSP 44F 'gK RM" RM!V3RlSP 444'gR#R#)a0Returns True if the graph G is a triad, else False. Parameters ---------- G : graph A NetworkX Graph Returns ------- istriad : boolean Whether G is a valid triad Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1)]) >>> nx.is_triad(G) True >>> G.add_edge(0, 1) >>> nx.is_triad(G) False c3L<"TFqV3SP49xK R#5ir )edges)r rrs& rris_triad..2s>Iq1v*Is!$TF) isinstancenxGraphorder is_directedanyr1)rsfris_triadr]sd.!RXX 779>bnnQ//3>AGGI>333>AGGI>>> rT) returns_graphc#"\VP4^4pVF$pVPV4P4xK& R#5i)aA generator of all possible triads in G. Parameters ---------- G : digraph A NetworkX DiGraph Returns ------- all_triads : generator of DiGraphs Generator of triads (order-3 DiGraphs) Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1), (3, 4), (4, 1), (4, 2)]) >>> for triad in nx.all_triads(G): ... print(triad.edges) [(1, 2), (2, 3), (3, 1)] [(1, 2), (4, 1), (4, 2)] [(3, 1), (3, 4), (4, 1)] [(2, 3), (3, 4), (4, 2)] N)rr1subgraphcopy)rtripletstriplets& r all_triadsrd7s;4AGGIq)Hjj!&&((sAA c\V4p\\4pVF%p\V4pW$,P V4K' V#)aRReturns a list of all triads for each triad type in a directed graph. There are exactly 16 different types of triads possible. Suppose 1, 2, 3 are three nodes, they will be classified as a particular triad type if their connections are as follows: - 003: 1, 2, 3 - 012: 1 -> 2, 3 - 102: 1 <-> 2, 3 - 021D: 1 <- 2 -> 3 - 021U: 1 -> 2 <- 3 - 021C: 1 -> 2 -> 3 - 111D: 1 <-> 2 <- 3 - 111U: 1 <-> 2 -> 3 - 030T: 1 -> 2 -> 3, 1 -> 3 - 030C: 1 <- 2 <- 3, 1 -> 3 - 201: 1 <-> 2 <-> 3 - 120D: 1 <- 2 -> 3, 1 <-> 3 - 120U: 1 -> 2 <- 3, 1 <-> 3 - 120C: 1 -> 2 -> 3, 1 <-> 3 - 210: 1 -> 2 <-> 3, 1 <-> 3 - 300: 1 <-> 2 <-> 3, 1 <-> 3 Refer to the :doc:`example gallery ` for visual examples of the triad types. Parameters ---------- G : digraph A NetworkX DiGraph Returns ------- tri_by_type : dict Dictionary with triad types as keys and lists of triads as values. Examples -------- >>> G = nx.DiGraph([(1, 2), (1, 3), (2, 3), (3, 1), (5, 6), (5, 4), (6, 7)]) >>> dict = nx.triads_by_type(G) >>> dict["120C"][0].edges() OutEdgeView([(1, 2), (1, 3), (2, 3), (3, 1)]) >>> dict["012"][0].edges() OutEdgeView([(1, 2)]) References ---------- .. [1] Snijders, T. (2012). "Transitivity and triads." University of Oxford. https://web.archive.org/web/20170830032057/http://www.stats.ox.ac.uk/~snijders/Trans_Triads_ha.pdf )rdrlist triad_typeappend)rall_tri tri_by_typetriadrBs& rtriads_by_typerlVsEnmGd#K%   ' rc\V4'g\P!R4h\VP 44pV^8XdR#V^8XdR#V^8XdVP 4wr#\ V4\ V48XdR#V^,V^,8XdR#V^,V^,8XdR#V^,V^,8XgV^,V^,8XdR#R#V^8Xd\ VP 4^4Fwr#p\ V4\ V48XdV^,V9dR#R #\ V4P\ V44\ V48XgKfV^,V^,V^,0V^,V^,V^,0u;8Xd"\ VP448Xd R #R #R # R#V^8XEd\ VP 4^4Fwr#rE\ V4\ V48XgK!\ V4\ V48XdR #V^,0V^,0u;8Xd,\ V4P\ V448XdR #V^,0V^,0u;8Xd,\ V4P\ V448XdR#V^,V^,8XgKR# R#V^8XdR#V^8XdR#R#)a\Returns the sociological triad type for a triad. Parameters ---------- G : digraph A NetworkX DiGraph with 3 nodes Returns ------- triad_type : str A string identifying the triad type Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1)]) >>> nx.triad_type(G) '030C' >>> G.add_edge(1, 3) >>> nx.triad_type(G) '120C' Notes ----- There can be 6 unique edges in a triad (order-3 DiGraph) (so 2^^6=64 unique triads given 3 nodes). These 64 triads each display exactly 1 of 16 topologies of triads (topologies can be permuted). These topologies are identified by the following notation: {m}{a}{n}{type} (for example: 111D, 210, 102) Here: {m} = number of mutual ties (takes 0, 1, 2, 3); a mutual tie is (0,1) AND (1,0) {a} = number of asymmetric ties (takes 0, 1, 2, 3); an asymmetric tie is (0,1) BUT NOT (1,0) or vice versa {n} = number of null ties (takes 0, 1, 2, 3); a null tie is NEITHER (0,1) NOR (1,0) {type} = a letter (takes U, D, C, T) corresponding to up, down, cyclical and transitive. This is only used for topologies that can have more than one form (eg: 021D and 021U). References ---------- .. [1] Snijders, T. (2012). "Transitivity and triads." University of Oxford. https://web.archive.org/web/20170830032057/http://www.stats.ox.ac.uk/~snijders/Trans_Triads_ha.pdf z"G is not a triad (order-3 DiGraph)r+r*r)021D021U021C111U111D030C030T201120D120U120C210300N) r]rXNetworkXAlgorithmErrorr.rUr,rsymmetric_differencer1 intersection)r num_edgese1e2e3e4s& rrgrgs>f A;;''(LMMAGGIIA~ a a r7c"g  Ube^ Ube^ Ube^r!u1~ . a&qwwy!4JBB2w#b'!a5B;!R--c"g6#b'AqE2a5"Q%(RUBqE2a5,ASS^S!T5 a*1779a8NBB2w#b'!r7c"g% qE7r!ugFR)=)=c"g)FF!GqE7r!ugFR)=)=c"g)FF!Ga5BqE>!9 a a r)rRr]rdrlrg)@r!rrrrrrr rrrrr r r rrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr)r+r*r)rnrorprrrqrtrsrurvrwrxryrzr )__doc__ collectionsr itertoolsrrnetworkxrXnetworkx.utilsrr__all__TRICODESr6r0r7r _dispatchablerRr]rdrlrg)rrLs00rrs( 1#0? A J *