a J5d4@sdZddlmZddlmZmZddlmZddlZ ddl m Z gdZ dZ d Zd d ee DZd d Ze ddddZddZe dddZe dddZe dddZe dddZe dddZdS)z*Functions for analyzing triads of a graph.) defaultdict) combinations permutations)sampleN)not_implemented_for)triadic_censusis_triad all_triplets all_triadstriads_by_type triad_type random_triad)@rrrrrrr rrrrr r r rrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr)003012102021D021U021C111D111U030T030C201120D120U120C210300cCsi|]\}}|t|dqS)r) TRIAD_NAMES).0icoder2V/var/www/html/django/DPS/env/lib/python3.9/site-packages/networkx/algorithms/triads.py ur4csJ||df||df||df||df||df||dff}tfdd|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 c3s$|]\}}}||vr|VqdSNr2)r/uvxGr2r3 r5z_tricode..)sum)r<r9r8wZcombosr2r;r3_tricodexs4r@Z undirectedcs.t||dur.t|tkr.tdtt}ddtD}|r~j}|fddt|DfddD}fddD|rfd d|Dtfd d|D}|d }tfd d|D}|d } d dtD} D]} || } | } |r6d}}}}| D]^}|||| krVq:||}| |B|| h}|D]p}||||ks|| ||kr||krrnn0| ||vrrt | ||}| t |d7<qr|| vr | dt|d 7<n| dt|d 7<|r:|vr:|}|t|| @7}|t|| 7}|}|t|| @7}|t|| 7}q:|r | d|||d 7<| d| ||d 7<q dd d}||d|d d}||}|t| | d<| S)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. 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|]\}}||qSr2r2r/r0nr2r2r3r4r5z"triadic_census..c3s|]\}}||fVqdSr7r2rA)Nr2r3r=r5z!triadic_census..cs*i|]"}|j|j|BqSr2predkeyssuccr/rBr;r2r3r4r5cs*i|]"}|j|j|@qSr2rDrHr;r2r3r4r5cs*i|]"}|j|j|AqSr2rDrHr;r2r3r4r5c3s(|] }|D]}|vrdVqqdSrNr2r/rBZnbr)nodesetsgl_nbrsr2r3r=r5rc3s(|] }|D]}|vrdVqqdSrIr2rJ)dbl_nbrsrKr2r3r=r5cSsi|] }|dqS)rr2)r/namer2r2r3r4r5rrr rrr) setZ nbunch_iterlen ValueError enumeratenodesupdater>r.r@TRICODE_TO_NAMEvalues)r<ZnodelistZNnotmZ not_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_nodesetZ total_censusr2)r<rCrMrKrLr3rsd+    H  rcsDttjr@dkr@tr@tfddDs@dSdS)zReturns 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 rc3s|]}||fvVqdSr7)edgesrHr;r2r3r=r5zis_triad..TF) isinstancenxZGraphorderZ is_directedanyrSr;r2r;r3rs rcCst|d}|S)zReturns 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 r)rrS)r<tripletsr2r2r3r sr ccs,t|d}|D]}||VqdS)zA 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) rN)rrSsubgraphcopy)r<r]tripletr2r2r3r %sr cCs4t|}tt}|D]}t|}|||q|S)a Returns a list of all triads for each triad type in a directed graph. Parameters ---------- G : digraph A NetworkX DiGraph Returns ------- tri_by_type : dict Dictionary with triad types as keys and lists of triads as values. )r rlistr append)r<Zall_triZ tri_by_typeZtriadrNr2r2r3r 8s r cCstt|stdt|}|dkr*dS|dkr6dS|dkr|\}}t|t|kr^dS|d|dkrrdS|d|dkrd S|d|dks|d|dkrd Sn|d krpt|d D]\}}}t|t|kr|d|vrd Sd St|t|t|kr|d|d|dh|d|d|dhkrZt|krdnndSdSqƐn|dkrTt|dD]\}}}}t|t|krt|t|krdS|dh|dhkrt| t|krnndS|dh|dhkr,t| t|kr6nndS|d|dkrdSqn|dkrbdS|dkrpdSdS)aMReturns 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 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 assymmetric ties (takes 0, 1, 2, 3); an assymmetric 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) rrZZNetworkXAlgorithmErrorrPrXrOrsymmetric_differencerS intersection)r<Z num_edgese1e2Ze3Ze4r2r2r3r PsT)     H  66   r cCs tt|d}||}|S)zReturns a random triad from a directed graph. Parameters ---------- G : digraph A NetworkX DiGraph Returns ------- G2 : subgraph A randomly selected triad (order-3 NetworkX DiGraph) r)rrarSr^)r<rSZG2r2r2r3r s r )N)__doc__ collectionsr itertoolsrrrandomrZnetworkxrZZnetworkx.utilsr__all__ZTRICODESr.rRrUr@rrr r r r r r2r2r2r3s0    E  z    W