a º”h<ã@sdZddlmZddlmZmZddlZddlm Z m Z gd¢ZdZdZ d d „eeƒDƒZdd„Ze d ƒejddd„ƒƒZejdd„ƒZe d ƒejdd„ƒƒZe d ƒejdd„ƒƒZe d ƒejdd„ƒƒZe d ƒejdd„ƒƒZe d ƒe dƒejddd„ƒƒƒZdS)z*Functions for analyzing triads of a graph.é)Údefaultdict)ÚcombinationsÚpermutationsN)Únot_implemented_forÚpy_random_state)Útriadic_censusÚis_triadÚall_tripletsÚ all_triadsÚtriads_by_typeÚ triad_typeÚrandom_triad)@éérérééérréérrrérrrrré ré ré rérréérrrrrrrrrrrrrrrrrrrrrrrrrrrrrrré)Ú003Ú012Ú102Ú021DÚ021UÚ021CÚ111DÚ111UÚ030TÚ030CÚ201Ú120DÚ120UÚ120CÚ210Ú300cCsi|]\}}|t|d“qS)r)ÚTRIAD_NAMES)Ú.0ÚiÚcode©r2úH/var/www/auris/lib/python3.9/site-packages/networkx/algorithms/triads.pyÚ tór4csJ||df||df||df||df||df||dff}t‡fdd„|DƒƒS) zñReturns 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. rrrrré c3s$|]\}}}|ˆ|vr|VqdS©Nr2)r/ÚuÚvÚx©ÚGr2r3Ú €r5z_tricode..)Úsum)r<r9r8ÚwZcombosr2r;r3Ú_tricodews4r@Z undirectedcs.tˆ |¡ƒ‰|dur.t|ƒtˆƒkr.tdƒ‚tˆƒ‰ˆtˆƒ}dd„tˆƒDƒ}|r~ˆjˆ}| ‡fdd„t|ƒDƒ¡‡fdd„ˆDƒ}‡fdd„ˆDƒ‰|rø‡fd d„|Dƒ‰t‡‡fd d„|Dƒƒ}|d}t‡‡fdd„|Dƒƒ}|d} d d„tDƒ} ˆD]Ð}||}ˆ|} |r6d}}}}|D]^}||||krVq:||}||B||h}|D]p}||||ks¾||||kr¬||krrnn0|||vrrt ˆ|||ƒ}| t |d7<qr|| vr| dˆt|ƒd7<n| dˆt|ƒd7<|r:|ˆvr:ˆ|}|t||ˆ@ƒ7}|t||ˆƒ7}ˆ|}|t||ˆ@ƒ7}|t||ˆƒ7}q:|r | d|||d7<| d| ||d7<q ˆˆdˆdd}||d|dd}||}|t| ¡ƒ| d<| S)abDetermines 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. 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 GcSsi|]\}}||“qSr2r2©r/r0Únr2r2r3r4Ïr5z"triadic_census..c3s|]\}}||ˆfVqdSr7r2rA)ÚNr2r3r=Ór5z!triadic_census..cs*i|]"}|ˆj| ¡ˆj| ¡B“qSr2©ÚpredÚkeysÚsucc©r/rBr;r2r3r4Ør5cs*i|]"}|ˆj| ¡ˆj| ¡@“qSr2rDrHr;r2r3r4Ùr5cs*i|]"}|ˆj| ¡ˆj| ¡A“qSr2rDrHr;r2r3r4Ür5c3s(|] }ˆ|D]}|ˆvrdVqqdS©rNr2©r/rBZnbr)ÚnodesetÚsgl_nbrsr2r3r=Þr5rc3s(|] }ˆ|D]}|ˆvrdVqqdSrIr2rJ)Údbl_nbrsrKr2r3r=àr5cSsi|] }|d“qS)rr2)r/Únamer2r2r3r4är5rrr rrr)ÚsetZnbunch_iterÚlenÚ ValueErrorÚ enumerateÚnodesÚupdater>r.r@ÚTRICODE_TO_NAMEÚvalues)r<ZnodelistZNnotÚmZnot_nodesetZnbrsZsglZsgl_edges_outsideZdblZdbl_edges_outsideZcensusr9ZvnbrsZ dbl_vnbrsZ sgl_unbrs_bdyZ sgl_unbrs_outZ dbl_unbrs_bdyZ dbl_unbrs_outr8ZunbrsZ neighborsr?r1Z sgl_unbrsZ dbl_unbrsZtotal_trianglesZtriangles_without_nodesetZtotal_censusr2)r<rCrMrKrLr3rƒsdD H rcsDtˆtjƒr@ˆ ¡dkr@t ˆ¡r@t‡fdd„ˆ ¡Dƒƒs@dSdS)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 rc3s|]}||fˆ ¡vVqdSr7)ÚedgesrHr;r2r3r=0r5zis_triad..TF)Ú isinstanceÚnxZGraphÚorderZis_directedÚanyrSr;r2r;r3rs rcCst| ¡dƒ}|S)a’Returns a generator of all possible sets of 3 nodes in a DiGraph. 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)] r)rrS)r<Útripletsr2r2r3r 5sr ccs,t| ¡dƒ}|D]}| |¡ ¡VqdS)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)rrSÚsubgraphÚcopy)r<r]Ztripletr2r2r3r Osr cCs4t|ƒ}ttƒ}|D]}t|ƒ}|| |¡q|S)aþReturns 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 rÚlistrÚappend)r<Zall_triZtri_by_typeZtriadrNr2r2r3rns7rcCstt|ƒst d¡‚t| ¡ƒ}|dkr*dS|dkr6dS|dkr®| ¡\}}t|ƒt|ƒkr^dS|d|dkrrdS|d|dkr†d S|d|dks¦|d|dkrªd SnÂ|dkrpt| ¡dƒD]¤\}}}t|ƒt|ƒkrü|d|vrödSd St|ƒ t|ƒ¡t|ƒkrÆ|d|d|dh|d|d|dhkrZt| ¡ƒkrdnndSdSqÆn|dkrTt| ¡dƒD]È\}}}}t|ƒt|ƒkrˆt|ƒt|ƒkr¾dS|dh|dhkrðt|ƒ t|ƒ¡krúnndS|dh|dhkr,t|ƒ t|ƒ¡kr6nndS|d|dkrˆdSqˆn|dkrbdS|dkrpdSdS)aøReturns 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)rrrrrr r!r"r#rr%r$r'r&rr(r)r*r+rr,rr-N) rrZZNetworkXAlgorithmErrorrPrXrOrÚsymmetric_differencerSÚintersection)r<Z num_edgesÚe1Úe2Ze3Ze4r2r2r3rsT3 H 66 rrcCsDt|ƒdkr"t dt|ƒ›d¡‚| t| ¡ƒd¡}| |¡}|S)a—Returns a random triad from a directed graph. 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)]) rz2G needs at least 3 nodes to form a triad; (it has z nodes))rPrZZ NetworkXErrorÚsampler`rSr^)r<ÚseedrSZG2r2r2r3r s ÿ r )N)N)Ú__doc__ÚcollectionsrÚ itertoolsrrZnetworkxrZZnetworkx.utilsrrÚ__all__ZTRICODESr.rRrUr@Ú _dispatchrrr r rrr r2r2r2r3Ús> E =`