U 9v f?@sdZddlmZddlmZmZddlZddlm Z m Z dddd d d d gZ d Z dZ ddee DZddZe ddddZeddZe dddZe ddd Ze ddd Ze ddd Ze de dddd ZdS)z*Functions for analyzing triads of a graph.) defaultdict) combinations permutationsN)not_implemented_forpy_random_statetriadic_censusis_triad all_triplets all_triadstriads_by_type triad_type random_triad)@rrrrrrr rrrrr r r rrr rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr)003012102021D021U021C111D111U030T030C201120D120U120C210300cCsi|]\}}|t|dqS)r) TRIAD_NAMES).0icoder2>/tmp/pip-unpacked-wheel-_lngutwb/networkx/algorithms/triads.py tsr4csJ||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$|]\}}}||kr|VqdSNr2)r/uvxGr2r3 s z_tricode..)sum)r;r8r7wZcombosr2r:r3_tricodews4r?Z undirectedcs.t||dk r.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| ||krrt | ||}| t |d7<qr|| kr | dt|d 7<n| dt|d 7<|r:|kr:|}|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)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|]\}}||qSr2r2r/r0nr2r2r3r4sz"triadic_census..c3s|]\}}||fVqdSr6r2r@)Nr2r3r<sz!triadic_census..cs*i|]"}|j|j|BqSr2predkeyssuccr/rAr:r2r3r4scs*i|]"}|j|j|@qSr2rCrGr:r2r3r4scs*i|]"}|j|j|AqSr2rCrGr:r2r3r4sc3s(|] }|D]}|krdVqqdSrNr2r/rAZnbr)nodesetsgl_nbrsr2r3r<s  rc3s(|] }|D]}|krdVqqdSrHr2rI)dbl_nbrsrJr2r3r<s  cSsi|] }|dqS)rr2)r/namer2r2r3r4srrr rrr) setZ nbunch_iterlen ValueError enumeratenodesupdater=r.r?TRICODE_TO_NAMEvalues)r;ZnodelistZNnotmZ not_nodesetZnbrsZsglZsgl_edges_outsideZdblZdbl_edges_outsideZcensusr8ZvnbrsZ dbl_vnbrsZ sgl_unbrs_bdyZ sgl_unbrs_outZ dbl_unbrs_bdyZ dbl_unbrs_outr7ZunbrsZ neighborsr>r1Z sgl_unbrsZ dbl_unbrsZtotal_trianglesZtriangles_without_nodesetZ total_censusr2)r;rBrLrJrKr3rsdC    H  csDttjr@dkr@tr@tfddDs@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|]}||fkVqdSr6)edgesrGr:r2r3r</szis_triad..TF) isinstancenxZGraphorderZ is_directedanyrRr:r2r:r3rs  cCst|d}|S)aReturns 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)rrR)r;tripletsr2r2r3r 4sccs,t|d}|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)rrRsubgraphcopy)r;r\Ztripletr2r2r3r MscCs4t|}tt}|D]}t|}|||q|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;Zall_triZ tri_by_typeZtriadrMr2r2r3r ks 6cCstt|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|krd 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)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)rrrrrr r!r"r#rr%r$r'r&rr(r)r*r+rr,rr-N) rrYZNetworkXAlgorithmErrorrOrWrNrsymmetric_differencerR intersection)r;Z num_edgese1e2Ze3Ze4r2r2r3r sT2     H  66   rcCs"|t|d}||}|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) 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)]) r)sampler_rRr])r;seedrRZG2r2r2r3r s )N)N)__doc__ collectionsr itertoolsrrZnetworkxrYZnetworkx.utilsrr__all__ZTRICODESr.rQrTr?r _dispatchrr r r r r r2r2r2r3sB  E      = `