D^(hAZdZddlmZddlmZmZddlZddlm Z m Z gdZ dZ dZ ee Dcic]\}}|e |d z c}}Zd Ze d ej"dd Zej"d Ze d ej"dZe d ej"ddZe d ej"dZe d ej"dZe d e d ej"ddddZycc}}w)z*Functions for analyzing triads of a graph.) defaultdict) combinations permutationsN)not_implemented_forpy_random_state)triadic_censusis_triad all_triplets all_triadstriads_by_type triad_type random_triad)@rrrrrrr rrrrr r r rrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr)003012102021D021U021C111D111U030T030C201120D120U120C210300rc`||df||df||df||df||df||dff}tfd|DS)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. rrrrr c3:K|]\}}}||vs|ywN).0uvxGs X/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/networkx/algorithms/triads.py z_tricode..s!4WQ1!qt)q4s)sum)r8r6r5wcomboss` r9_tricoder>wsL!Qi!QQ1I1ay1a*q!Rj QF 44 44 undirectedc 6 !"t|j|!|"t|t!k7r tdt|t!z }t !Dcic]\}}|| }}}|r2|j !z }|j fdt |D|Dcic]>}||j|j|j|jz@}}|Dcic]>}||j|j|j|jz@c} |r~Dcic]>}||j|j|j|jz @c}"t!"fd|D}|dz} t !fd|D} | dz} tD cic]} | d} } !D]^}||} |}|rdx}x}x}}|D]}||||kr||}||z||hz }|D]O}||||ks ||||cxkr ||ks#n&|||vs.t||||}| t|xxdz cc<Q||vr| dxxt|z dz z cc<n| d xxt|z dz z cc<|s|!vs"|}t||!z zz }t||z !z z } |}t||!z zz }t||z !z z }|s3| d xx dzzz z cc<| dxx dzzz z cc<adz zdz zd z}||dz z|dz zd z}||z }|t| jz | d <| Scc}}wcc}wcc}wcc}wcc} w) amDetermines 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 Gc32K|]\}}||zfywr2r3)r4inNs r9r:z!triadic_census..s?1!QU?sc3@K|]}|D] }|vsd ywrNr3)r4rDnbrnodesetsgl_nbrss r9r:z!triadic_census..(VHQKVS3gCU!V!V rc3@K|]}|D] }|vsd ywrGr3)r4rDrHdbl_nbrsrIs r9r:z!triadic_census..rKrLrrr!r rr)set nbunch_iterlen ValueError enumeratenodesupdatepredkeyssuccr; TRIAD_NAMESr>TRICODE_TO_NAMEvalues)#r8nodelistNnotrCrDm not_nodesetnbrssglsgl_edges_outsidedbldbl_edges_outsidenamecensusr6vnbrs dbl_vnbrs sgl_unbrs_bdy sgl_unbrs_out dbl_unbrs_bdy dbl_unbrs_outr5unbrs neighborsr<code sgl_unbrs dbl_unbrstotal_trianglestriangles_without_nodeset total_censusrErNrIrJs# @@@@r9rrsP!--)*GH W =NOO AA s7| D$G,-$!QA-A- gg'  ? +(>?? => >qAqvvay~~!&&).."22 2 >D >@AB1166!9>>#affQinn&666BH DOPqAqvvay~~'!&&)..*:::PV[VV1HV[VV1H#. .$dAg .F . %VQQK LM MM MM MMM BAtqt|GE1a&0I 7Q4!A$;1Q4!A$#51#5!47:J#Aq!Q/D?401Q61 7 I~u S^!3a!77 u S^!3a!77 ($QK Y%@!AA Y%6%@!AA $QK Y%@!AA Y%6%@!AA 5 B8  5M.--STBT2TU UM 5M.--STBT2TU UMK%VRAE{a!e,2O!%!2dQh!?A E"%>>L 3v}}#77F5M MK . ?BQ/s!* N2AN;AN AN NcttjrKjdk(r8tjr#t fdj Dsyy)atReturns True if the graph G is a triad, else False. Parameters ---------- G : graph A NetworkX Graph Returns ------- istriad : boolean Whether G is a valid triad Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 1)]) >>> nx.is_triad(G) True >>> G.add_edge(0, 1) >>> nx.is_triad(G) False rc3FK|]}||fjvywr2)edges)r4rDr8s r9r:zis_triad..4s >q1v*>s!TF) isinstancenxGraphorder is_directedanyrT)r8s`r9r r sE.!RXX 779>bnnQ/>AGGI>> r?crddl}|jdtdt|j d}|S)a`Returns a generator of all possible sets of 3 nodes in a DiGraph. .. deprecated:: 3.3 all_triplets is deprecated and will be removed in NetworkX version 3.5. Use `itertools.combinations` instead:: all_triplets = itertools.combinations(G, 3) Parameters ---------- G : digraph A NetworkX DiGraph Returns ------- triplets : generator of 3-tuples Generator of tuples of 3 nodes Examples -------- >>> G = nx.DiGraph([(1, 2), (2, 3), (3, 4)]) >>> list(nx.all_triplets(G)) [(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)] rNze all_triplets is deprecated and will be removed in v3.5. Use `itertools.combinations(G, 3)` instead.rcategory stacklevelr)warningswarnDeprecationWarningrrT)r8rtripletss r9r r 9s>: MM :$ AGGIq)H Or?T) returns_graphc#Kt|jd}|D]#}|j|j%yw)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)r8rtriplets r9r r dsA4AGGIq)H)jj!&&(()sAAct|}tt}|D]!}t|}||j |#|S)aReturns 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)r8all_tri tri_by_typetriadres r9r r sLnmGd#K(% D  '( r?ct|stjdt|j }|dk(ry|dk(ry|dk(r[|j \}}t |t |k(ry|d|dk(ry|d|dk(ry |d|dk(s |d|dk(ry y|d k(rt |j d D]\}}}t |t |k(r |d|vry y t |jt |t |k(sY|d|d|dh|d|d|dhcxk(rt |jk(ryyyy|dk(rt |j dD]\}}}}t |t |k(s t |t |k(ry|dh|dhcxk(r't |jt |k(ry|dh|dhcxk(r't |jt |k(ry|d|dk(syy|dk(ry|dk(ryy)aReturns 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)rrrr rr!r"r#r$rr&r%r(r'rr)r*r+r,rr-rr.N) r ryNetworkXAlgorithmErrorrQrwrOrsymmetric_differencerT intersection)r8 num_edgese1e2e3e4s r9r r sNf A;''(LMMAGGIIA~ a aB r7c"g  Ube^ Ube^ Ube^r!u1~ . a&qwwy!4 JBB2w#b'!a5B;!R--c"g6#b'AqE2a5"Q%(RUBqE2a5,ASS^S!T  a*1779a8 "NBB2w#b'!r7c"g% qE7r!ugFR)=)=c"g)FF!GqE7r!ugFR)=)=c"g)FF!Ga5BqE>! " a a r?)preserve_all_attrsrcddl}|jdtdt|dkr"t j dt|d|j t|jd}|j|}|S) aVReturns a random triad from a directed graph. .. deprecated:: 3.3 random_triad is deprecated and will be removed in version 3.5. Use random sampling directly instead:: G.subgraph(random.sample(list(G), 3)) Parameters ---------- G : digraph A NetworkX DiGraph seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- G2 : subgraph A randomly selected triad (order-3 NetworkX DiGraph) Raises ------ NetworkXError If the input Graph has less than 3 nodes. Examples -------- >>> G = nx.DiGraph([(1, 2), (1, 3), (2, 3), (3, 1), (5, 6), (5, 4), (6, 7)]) >>> triad = nx.random_triad(G, seed=1) >>> triad.edges OutEdgeView([(1, 2)]) rNz random_triad is deprecated and will be removed in NetworkX v3.5. Use random.sample instead, e.g.:: G.subgraph(random.sample(list(G), 3)) rrrz2G needs at least 3 nodes to form a triad; (it has z nodes)) rrrrQry NetworkXErrorsamplerrTr)r8seedrrTG2s r9rr$sN MM 8$ 1vz@Q P   KKQWWY +E E B Ir?r2)__doc__ collectionsr itertoolsrrnetworkxrynetworkx.utilsrr__all__TRICODESrYrSrZr> _dispatchablerr r r r r r)rCros00r9rs 1#0? 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