ó |£*^c@sÃdZddlmZddlZddlmZdjdddd gƒZd d d d dgZdd„Z dd„Z ddd„Z dde d„Zddd„Zd„Zdd„ZdS(s>Algorithms to characterize the number of triangles in a graph.iÿÿÿÿ(t combinationsN(t NetworkXErrors s%Aric Hagberg s Dan Schult (dschult@colgate.edu)sPieter Swart (swart@lanl.gov)s%Jordi Torrents t trianglestaverage_clusteringt clusteringt transitivitytsquare_clusteringcCs_|jƒrtdƒ‚n||krBtt||ƒƒddStd„t||ƒDƒƒS(s Compute the number of triangles. Finds the number of triangles that include a node as one vertex. Parameters ---------- G : graph A networkx graph nodes : container of nodes, optional (default= all nodes in G) Compute triangles for nodes in this container. Returns ------- out : dictionary Number of triangles keyed by node label. Examples -------- >>> G=nx.complete_graph(5) >>> print(nx.triangles(G,0)) 6 >>> print(nx.triangles(G)) {0: 6, 1: 6, 2: 6, 3: 6, 4: 6} >>> print(list(nx.triangles(G,(0,1)).values())) [6, 6] Notes ----- When computing triangles for the entire graph each triangle is counted three times, once at each node. Self loops are ignored. s/triangles() is not defined for directed graphs.icss(|]\}}}||dfVqdS(iN((t.0tvtdtt((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pys 9s(t is_directedRtnextt_triangles_and_degree_itertdict(tGtnodes((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyRs !  c #síˆjƒrtdƒ‚n|dkr9ˆjjƒ}n‡fd†ˆj|ƒDƒ}xŽ|D]†\}}t|ƒt|gƒ}d}xD|D]<}tˆ|ƒt|gƒ}|t|j|ƒƒ7}q‘W|t|ƒ|fVq_WdS(s¹ Return an iterator of (node, degree, triangles). This double counts triangles so you may want to divide by 2. See degree() and triangles() for definitions and details. sNot defined for multigraphs.c3s|]}|ˆ|fVqdS(N((Rtn(R(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pys HsiN( t is_multigraphRtNonetadjtitemst nbunch_itertsettlent intersection( RRt nodes_nbrsRtv_nbrstvst ntrianglestwtws((Rso/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyR ;s   tweightc#sÈjƒrtdƒ‚nˆd ks9ˆjƒgkrBd}n.tt‡fd†ˆjdtƒDƒƒƒ}|d krŽˆjjƒ}n‡fd†ˆj |ƒDƒ}x|D]\}}t |ƒt |gƒ}d}t ƒ} x¸|D]°} ˆ|| j ˆdƒ|} | j | ƒt ˆ| ƒ| } xh|| @D]\} ˆ| | j ˆdƒ|}ˆ|| j ˆdƒ|}|| ||dd7}q?WqïW|t |ƒ|dfVq´Wd S( si Return an iterator of (node, degree, weighted_triangles). Used for weighted clustering. sNot defined for multigraphs.gð?c3s*|] \}}}|jˆdƒVqdS(gð?N(tget(RtuRR (R (so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pys _stdatac3s|]}|ˆ|fVqdS(N((RR(R(so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pys dsgg@iN(RRRtedgestfloattmaxtTrueRRRRR!taddR(RRR t max_weightRtitnbrstinbrstweighted_trianglestseentjtwijtjnbrstktwjktwki((RR so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyt#_weighted_triangles_and_degree_iterSs,      "cCsct||d|ƒjƒ}|sIg|D]}|dkr(|^q(}nt|ƒtt|ƒƒS(søCompute the average clustering coefficient for the graph G. The clustering coefficient for the graph is the average, .. math:: C = \frac{1}{n}\sum_{v \in G} c_v, where `n` is the number of nodes in `G`. Parameters ---------- G : graph nodes : container of nodes, optional (default=all nodes in G) Compute average clustering for nodes in this container. weight : string or None, optional (default=None) The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. count_zeros : bool If False include only the nodes with nonzero clustering in the average. Returns ------- avg : float Average clustering Examples -------- >>> G=nx.complete_graph(5) >>> print(nx.average_clustering(G)) 1.0 Notes ----- This is a space saving routine; it might be faster to use the clustering function to get a list and then take the average. Self loops are ignored. References ---------- .. [1] Generalizations of the clustering coefficient to weighted complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela, K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007). http://jponnela.com/web_documents/a9.pdf .. [2] Marcus Kaiser, Mean clustering coefficients: the role of isolated nodes and leafs on clustering measures for small-world networks. http://arxiv.org/abs/0802.2512 R i(RtvaluestsumR%R(RRR t count_zerostcR((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyRus5(cCsÇ|jƒrtddƒ‚n|dk r?t|||ƒ}nt||ƒ}i}xL|D]D\}}}|dkrƒd||>> G=nx.complete_graph(5) >>> print(nx.clustering(G,0)) 1.0 >>> print(nx.clustering(G)) {0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0} Notes ----- Self loops are ignored. References ---------- .. [1] Generalizations of the clustering coefficient to weighted complex networks by J. Saramäki, M. Kivelä, J.-P. Onnela, K. Kaski, and J. Kertész, Physical Review E, 75 027105 (2007). http://jponnela.com/web_documents/a9.pdf s&Clustering algorithms are not defined sfor directed graphs.igiN(R RRR5R R%tlistR6(RRR ttd_itertclustercRR R ((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyR¯s=       cCsjd}d}x9t|ƒD]+\}}}|||d7}||7}qW|dkrXdS|t|ƒSdS(sæCompute graph transitivity, the fraction of all possible triangles present in G. Possible triangles are identified by the number of "triads" (two edges with a shared vertex). The transitivity is .. math:: T = 3\frac{\#triangles}{\#triads}. Parameters ---------- G : graph Returns ------- out : float Transitivity Examples -------- >>> G = nx.complete_graph(5) >>> print(nx.transitivity(G)) 1.0 iigN(R R%(RRtcontriRR R ((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyRs c CsH|dkr|}n|j|ƒ}i}x÷|D]ï}d||>> G=nx.complete_graph(5) >>> print(nx.square_clustering(G,0)) 1.0 >>> print(nx.square_clustering(G)) {0: 1.0, 1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0} Notes ----- While `C_3(v)` (triangle clustering) gives the probability that two neighbors of node v are connected with each other, `C_4(v)` is the probability that two neighbors of node v share a common neighbor different from v. This algorithm can be applied to both bipartite and unipartite networks. References ---------- .. [1] Pedro G. Lind, Marta C. González, and Hans J. Herrmann. 2005 Cycles and clustering in bipartite networks. Physical Review E (72) 056127. giigð?iN(RRRRRR:R6( RRt node_iterRRt potentialR"Rtsquarestdegm((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyR&s&2     1  2  (t__doc__t itertoolsRtnetworkxtnxRtjoint __author__t__all__RRR R5R'RRRR(((so/home/gitlab-runner/builds/8480fa44/0/bergerc/fluidmanager-web/art-framework/bin/networkx/algorithms/cluster.pyts       ( ":Q &