~i7SrSSKJr SSKJrJr SSKrSSKJ r J r /SQr Sr Sr \"\ 5VVs0sHupU\ US - _M snnrS r\ "S 5\R"SS j55r\R"S 5r\ "S 5\R""SS9S55r\ "S 5\R"S55r\ "S 5\R"S55rgs snnf)z*Functions for analyzing triads of a graph.) defaultdict) combinations permutationsN)not_implemented_forpy_random_state)triadic_censusis_triad all_triadstriads_by_type triad_type)@rrrrrrr rrrrr r r rrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr)003012102021D021U021C111D111U030T030C201120D120U120C210300r cV^XS4X!S4XS4X1S4X#S4X2S44n[U4SjU55$)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. r rrrr c3B># UHupo2TU;dMUv M g7fN).0uvxGs W/home/mande/repo/quber/.venv/lib/python3.13/site-packages/networkx/algorithms/triads.py _tricode..~s4WQ1qt)qqs )sum)r6r4r3wcomboss` r7_tricoder=us@Qi!Q1Iay1*qRj QF 44 44 undirectedc ^^ ^!^"[URU55m!Ub#[U5[T!5:wa [S5e[U5mT[T!5- n[ T!5VVs0sHup4XC_M nnnU(a3UR T!- nUR U4Sj[ U555 UVs0sH>oDURUR5URUR5-_M@ nnUVs0sH>oDURUR5URUR5-_M@ snm U(aWVs0sH>oDURUR5URUR5- _M@ snm"[U!U"4SjU55nUS-n [U U!4SjU55n U S-n [V s0sHoS_M n n T!GH~nX~nT UnU(aS=n=n=nnUGH%nUUX^::aMUUnUU-UU1- nUHUnUUUU:d%X^UUs=:a UU:dM&O M*XU;dM4[XUU5nU [U==S- ss'MW UU;aU S==T[U5- S- - ss'OU S ==T[U5- S- - ss'U(dMUT!;dMT"UnW[UUT!- -5- nW[UU- T!- 5- nT UnW[UUT!- -5- nW[UU- T!- 5- nGM( U(dGMRU S ==W WWS--- - ss'U S==W WWS--- - ss'GM TTS- -TS- -S -nX"S- -US- -S -nUU- nU[U R55- U S 'U $s snnfs snfs snfs snfs sn f) 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 Gc34># UH upX!T-4v M g7fr0r1)r2inNs r7r8!triadic_census..s?(>!U(>sc3P># UHnTUHo"T;dM Sv M M g7fr Nr1)r2rCnbrnodesetsgl_nbrss r7r8rE$V[HQKSgCU!!K![& &rc3P># UHnTUHo"T;dM Sv M M g7frGr1)r2rCrHdbl_nbrsrIs r7r8rErKrLrr rrrr)set nbunch_iterlen ValueError enumeratenodesupdatepredkeyssuccr: TRIAD_NAMESr=TRICODE_TO_NAMEvalues)#r6nodelistNnotrBrCm not_nodesetnbrssglsgl_edges_outsidedbldbl_edges_outsidenamecensusr4vnbrs dbl_vnbrs sgl_unbrs_bdy sgl_unbrs_out dbl_unbrs_bdy dbl_unbrs_outr3unbrs neighborsr;code sgl_unbrs dbl_unbrstotal_trianglestriangles_without_nodeset total_censusrDrNrIrJs# @@@@r7rrsP!--)*GH W =NOO AA s7| D$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 $QK Y%@!AA Y%6%@!AA 58 4 5M.--STBT2TU UM 5M.--STBT2TU UMKRAE{a!e,2O!%!2dQh!?A E"%>>L 3v}}#77F5M MK . ?BQ/s!,N9;AN?AOAO  Oc^[T[R5(aXTR5S:XaD[R"T5(a)[ U4SjTR 555(dgg)a0Returns True if the graph G is a triad, else False. Parameters ---------- G : graph A NetworkX Graph Returns ------- istriad : boolean Whether G is a valid triad Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1)]) >>> nx.is_triad(G) True >>> G.add_edge(0, 1) >>> nx.is_triad(G) False rc3L># UHoU4TR5;v M g7fr0)edges)r2rCr6s r7r8is_triad..2s>Iq1v*Is!$TF) isinstancenxGraphorder is_directedanyrT)r6s`r7r r sN.!RXX 779>bnnQ//>AGGI>>> r>T) returns_graphc## [UR5S5nUH$nURU5R5v M& g7f)aA generator of all possible triads in G. Parameters ---------- G : digraph A NetworkX DiGraph Returns ------- all_triads : generator of DiGraphs Generator of triads (order-3 DiGraphs) Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1), (3, 4), (4, 1), (4, 2)]) >>> for triad in nx.all_triads(G): ... print(triad.edges) [(1, 2), (2, 3), (3, 1)] [(1, 2), (4, 1), (4, 2)] [(3, 1), (3, 4), (4, 1)] [(2, 3), (3, 4), (4, 2)] rN)rrTsubgraphcopy)r6tripletstriplets r7r r 7s;4AGGIq)Hjj!&&((sAAc[U5n[[5nUH!n[U5nX$R U5 M# U$)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 )r rlistr append)r6all_tri tri_by_typetriadres r7r r VsEnmGd#K%   ' r>c[U5(d[R"S5e[UR 55nUS:XagUS:XagUS:Xa_UR 5up#[ U5[ U5:XagUSUS:XagUSUS:Xag USUS:Xd USUS:Xag gUS :Xa[ UR 5S 5Hup#n[ U5[ U5:Xa USU;a g g [ U5R[ U55[ U5:XdM]USUSUS1USUSUS1s=:Xa[ UR55:Xa g g g gUS:Xa[ UR 5S5Hup#pE[ U5[ U5:XdM [ U5[ U5:Xa gUS1US1s=:Xa)[ U5R[ U55:Xa g US1US1s=:Xa)[ U5R[ U55:Xa g USUS:XdM g gUS:XagUS:Xagg)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)rrr rrrr r!r"rr$r#r&r%rr'r(r)r*rr+rr,N) r rzNetworkXAlgorithmErrorrQrwrOrsymmetric_differencerT intersection)r6 num_edgese1e2e3e4s r7r r s>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>r0)__doc__ collectionsr itertoolsrrnetworkxrznetworkx.utilsrr__all__TRICODESrYrSrZr= _dispatchablerr r r r )rBros00r7rs( 1#0? A J *