o hA@sdZddlmZddlmZmZddlZddlm Z m Z gdZ dZ dZ d d ee DZd d Ze d ejd ddZejddZe d ejddZe d ejddddZe d ejddZe d ejddZe d e dejdddd ddZdS)!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)003012102021D021U021C111D111U030T030C201120D120U120C210300cCsi|] \}}|t|dqS)r) TRIAD_NAMES).0icoder2n/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/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&|]\}}}||vr|VqdSNr2)r/uvxGr2r3 s$z_tricode..)sum)r;r8r7wcombosr2r:r3_tricodews4r@ undirectedcst||durt|tkrtdtt}ddtD}|r?j}|fddt|DfddD}fddD|r|fd d|Dtfd d|D}|d }tfd d|D}|d } d dtD} D]} || } | } |rd}}}}| D]}|||| krq||}| |B|| h}|D]3}||||ks|| ||kr||krnq| ||vrt | ||}| t |d7<q|| vr| dt|d 7<n| dt|d 7<|rA|vrA|}|t|| @7}|t|| 7}|}|t|| @7}|t|| 7}q|ra| d|||d 7<| d| ||d 7<qdd d}||d|d d}||}|t| | 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 GcSsi|]\}}||qSr2r2r/r0nr2r2r3r4sz"triadic_census..c3s |] \}}||fVqdSr6r2rB)Nr2r3r<z!triadic_census..cs*i|]}|j|j|BqSr2predkeyssuccr/rCr:r2r3r4*cs*i|]}|j|j|@qSr2rFrJr:r2r3r4rKcs*i|]}|j|j|AqSr2rFrJr:r2r3r4rKc3s*|]}|D] }|vrdVqqdSrNr2r/rCnbr)nodesetsgl_nbrsr2r3r<(rc3s*|]}|D] }|vrdVqqdSrLr2rM)dbl_nbrsrOr2r3r<rQcSsi|]}|dqS)rr2)r/namer2r2r3r4srrr rrr) set nbunch_iterlen ValueError enumeratenodesupdater=r.r@TRICODE_TO_NAMEvalues)r;nodelistNnotm not_nodesetnbrssglsgl_edges_outsidedbldbl_edges_outsidecensusr8vnbrs dbl_vnbrs sgl_unbrs_bdy sgl_unbrs_out dbl_unbrs_bdy dbl_unbrs_outr7unbrs neighborsr>r1 sgl_unbrs dbl_unbrstotal_trianglestriangles_without_nodeset total_censusr2)r;rDrRrOrPr3rsjH  @rcsDttjr 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 |] }||fvVqdSr6)edgesrJr:r2r3r<4rEzis_triad..TF) isinstancenxGraphorder is_directedanyrYr:r2r:r3rs rcCs*ddl}|jdtddt|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)warningswarnDeprecationWarningrrY)r;r~tripletsr2r2r3r 9sr T) returns_graphccs.t|d}|D] }||Vq 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)rrYsubgraphcopy)r;rtripletr2r2r3r ds r cCs4t|}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;all_tri tri_by_typetriadrSr2r2r3r s 7r cCs^t|s tdt|}|dkrdS|dkrdS|dkrW|\}}t|t|kr/dS|d|dkr9dS|d|dkrCd S|d|dksS|d|dkrUd SdS|d krt|d D]O\}}}t|t|kr{|d|vrxd Sd St|t|t|kr|d|d|dh|d|d|dhkrt|krdSdSdSqbdS|dkrt|dD]\\}}}}t|t|krt|t|krdS|dh|dhkrt| t|krdS|dh|dhkrt| t|krdS|d|dkrdSqdS|dkr&dS|dkr-dSdS)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) rrvNetworkXAlgorithmErrorrVrtrTrsymmetric_differencerY intersection)r; num_edgese1e2e3e4r2r2r3r sf3     >  ,0  r r)preserve_all_attrsrcCs\ddl}|jdtddt|dkrtdt|d|t|d}| |}|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)) rr{rz2G needs at least 3 nodes to form a triad; (it has z nodes)) r~rrrVrv NetworkXErrorsamplerrYr)r;seedr~rYG2r2r2r3r $s'  r r6)__doc__ collectionsr itertoolsrrnetworkxrvnetworkx.utilsrr__all__TRICODESr.rXr[r@ _dispatchablerrr r r r r r2r2r2r3s@  E   )   = `