\Mh7dZddlmZddlmZmZddlZddlm Z m Z gdZ dZ dZ d ee DZd Ze d ejdd Zejd Ze d ejddZe d ejdZe d ejdZdS)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)003012102021D021U021C111D111U030T030C201120D120U120C210300c6i|]\}}|t|dz S)r ) TRIAD_NAMES).0icodes Z/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/networkx/algorithms/triads.py r3rs'OOO41k$(+OOOcn||df||df||df||df||df||dff}tfd|DS)zReturns the integer code of the given triad. This is some fancy magic that comes from Batagelj and Mrvar's paper. It treats each edge joining a pair of `v`, `u`, and `w` as a bit in the binary representation of an integer. r rrrr c38K|]\}}}||v|VdSN)r/uvxGs r2 z_tricode..~s144WQ1!qt))q))))44r4)sum)r=r;r:wcomboss` r2_tricoderBus^!Qi!QQ1I1ay1a*q!Rj QF 4444444 4 44r4 undirectedc t||/t|tkrtdttz }dt D}|r8jz }|fdt |DfdD}fdD|rPfd|Dtfd|D}|d z}tfd |D}|d z} t td } D]} || } | } |rd x}x}x}}| D]Y}|||| kr||}| |z|| hz }|D]m}||||ks,|| ||cxkr ||kr:n6| ||vr-t| ||}| t|xxd z cc<n|| vr$| d xxt|z d z z cc<n#| dxxt|z d z z cc<|rt|vrp|}|t|| z zz }|t|| z z z }|}|t|| z zz }|t|| z z z }[|r2| dxx|||d zzz z cc<| d xx| ||d zzz z cc<d z zd z zdz}||d z z|d z zdz}||z }|t| z | d<| S)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 Nz3nodelist includes duplicate nodes or nodes not in Gci|]\}}|| Sr9r9)r/r0ns r2r3z"triadic_census..s---$!QA---r4c3,K|]\}}||zfVdSr8r9)r/r0rFNs r2r>z!triadic_census..s/??1!QU??????r4ci|]B}|j|j|zCSr9predkeyssuccr/rFr=s r2r3z"triadic_census..s@ > > >qAqvay~~!&).."2"22 > > >r4ci|]B}|j|j|zCSr9rJrNs r2r3z"triadic_census..s@BBB116!9>>##afQinn&6&66BBBr4ci|]B}|j|j|z CSr9rJrNs r2r3z"triadic_census..s@PPPqAqvay~~''!&)..*:*::PPPr4c3:K|]}|D] }|vdV dSr Nr9)r/rFnbrnodesetsgl_nbrss r2r>z!triadic_census..>VVHQKVVS3gCUCU!CUCUCUCUCUVVr4rc3:K|]}|D] }|vdV dSrRr9)r/rFrSdbl_nbrsrTs r2r>z!triadic_census..rVr4rr rrrr)set nbunch_iterlen ValueError enumeratenodesupdater?dictfromkeysr.rBTRICODE_TO_NAMEvalues) r=nodelistNnotm not_nodesetnbrssglsgl_edges_outsidedbldbl_edges_outsidecensusr;vnbrs dbl_vnbrs sgl_unbrs_bdy sgl_unbrs_out dbl_unbrs_bdy dbl_unbrs_outr:unbrs neighborsr@r1 sgl_unbrs dbl_unbrstotal_trianglestriangles_without_nodeset total_censusrHrXrTrUs ` @@@@r2rrsQP!--))**GH W = =NOOO AA s7|| D .-)G,,---A @g'  ???? +(>(>?????? ? > > >A > > >DBBBBBBBH %PPPPKPPPVVVVV[VVVVV1HVVVVV[VVVVV1H]]; * *F %V%VQQK  NLM MM MM MMM B BAtqt||GE1a&0I 7 7Q4!A$;;1Q4!A$#5#5#5#51#5#5#5#5#5!47:J:J#Aq!Q//D?40111Q6111I~~u S^^!3a!77 u S^^!3a!77  B(($QK Y%@!A!AA Y%6%@!A!AA $QK Y%@!A!AA Y%6%@!A!AA  V 5MMM.--STBT2TU UMMM 5MMM.--STBT2TU UMMMAE{a!e,2O!%!2dQh!?A E"%>>L 3v}}#7#77F5M Mr4cttjr[dkrCtjr/t fdDsdSdS)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 rc3HK|]}||fvVdSr8)edgesrNs r2r>zis_triad..2s4>>q1v*>>>>>>r4TF) isinstancenxGraphorder is_directedanyr^)r=s`r2r r so.!RX 7799>>bnQ//>>>>>AGGII>>>>> t 5r4T) returns_graphc#Kt|d}|D]+}||V,dS)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)rr^subgraphcopy)r=tripletstriplets r2r r 7s_4AGGIIq))H))jj!!&&(((((())r4ct|}tt}|D],}t|}|||-|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)r=all_tri tri_by_typetriadnames r2r r Vs[nmmGd##K((%  D  '''' r4c:t|stjdt|}|dkrdS|dkrdS|dkr|\}}t |t |krdS|d|dkrdS|d|dkrd S|d|dks|d|dkrd SdS|d krt |d D]\}}}t |t |kr|d|vrd Sd St |t |t |kr_|d|d|dh|d|d|dhcxkr%t |krnndSdSdS|dkr t |dD]\}}}}t |t |krt |t |krdS|dh|dhcxkr3t | t |krnndS|dh|dhcxkr3t | t |krnndS|d|dkrdSdS|dkrdS|dkrdSdS)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)rrr rrrr r!r"rr$r#r&r%rr'r(r)r*rr+rr,N) r rNetworkXAlgorithmErrorr[r}rYrsymmetric_differencer^ intersection)r= num_edgese1e2e3e4s r2r r s4f A;;N'(LMMMAGGIIIA~~u au aB r77c"gg  5 Ube^^6 Ube^^6 Ube^^r!u1~~6 .~ a&qwwyy!44  JBB2ww#b''!!a5B;;!66vvR--c"gg66#b''AAqE2a5"Q%(RUBqE2a5,ASSSSS^^SSSSS!66vv B   a*17799a88 " "NBB2ww#b''!!r77c"gg%% 55qE7r!ugFFFFR)=)=c"gg)F)FFFFFF!66qE7r!ugFFFFR)=)=c"gg)F)FFFFFF!66a5BqE>>!66 " " au au r4r8)__doc__ collectionsr itertoolsrrnetworkxrnetworkx.utilsrr__all__TRICODESr.r]rbrB _dispatchablerr r r r r9r4r2rs 10######00000000????????   A J *PO99X;N;NOOO 5 5 5\""SSS#"Sl:\""%%%))&%#"):\""::#":z\""]]#"]]]r4