ó ú£Õ\c@s¡dZddlZddlmZdZddddgZd dd d dd d „Zd ddd d„Z d dd d„Z d dd dd d„Z d„Z dS(s&PageRank analysis of graph structure. iÿÿÿÿN(t NetworkXErrorsAric Hagberg (hagberg@lanl.gov)tpageranktpagerank_numpytpagerank_scipyt google_matrixg333333ë?idg:Œ0âŽyE>tweightcst|ƒtjks*t|ƒtjkr9tdƒ‚nt|ƒdkrOiS|jƒsj|jƒ}n|}tj|d|ƒ}d|j ƒ} |d kr¶t j || ƒ} n=|} dt | jƒƒ} x| D]} | | c| 9>> G=nx.DiGraph(nx.path_graph(4)) >>> pr=nx.pagerank(G,alpha=0.9) Notes ----- The eigenvector calculation is done by the power iteration method and has no guarantee of convergence. The iteration will stop after max_iter iterations or an error tolerance of number_of_nodes(G)*tol has been reached. The PageRank algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs by converting each oriented edge in the directed graph to two edges. See Also -------- pagerank_numpy, pagerank_scipy, google_matrix References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry, The PageRank citation ranking: Bringing order to the Web. 1999 http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf s2pagerank() not defined for graphs with multiedges.iRgð?s7Personalization vector must have a value for every nodegc3s|]}ˆ|VqdS(N((t.0tn(txlast(sf/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/link_analysis/pagerank_alg.pys ~ss=pagerank: power iteration failed to convergein %d iterations.iN(ttypetnxt MultiGrapht MultiDiGrapht Exceptiontlent is_directedt to_directedtstochastic_graphtnumber_of_nodestNonetdicttfromkeystsumtvaluestsetRt out_degreetTruetkeystabs(tGtalphatpersonalizationtmax_iterttoltnstartRtDtWtscaletxtstktpRRtdangletit danglesumtnbrterr((Rsf/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/link_analysis/pagerank_alg.pyRsZC*      ) $ ,$ 1  cCsyddl}Wntk r/tdƒ‚nX|dkrK|jƒ}n3|jƒ}t|ƒt|ƒkr~tdƒ‚ntj|d|d|ƒ}|j \}}|dkr¸|S|j |j dd ƒdkƒ} x | dD]} d ||| >> G=nx.DiGraph(nx.path_graph(4)) >>> pr=nx.pagerank_numpy(G,alpha=0.9) Notes ----- The eigenvector calculation uses NumPy's interface to the LAPACK eigenvalue solvers. This will be the fastest and most accurate for small graphs. This implementation works with Multi(Di)Graphs. See Also -------- pagerank, pagerank_scipy, google_matrix References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry, The PageRank citation ranking: Bringing order to the Web. 1999 http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf iÿÿÿÿNs2pagerank_numpy() requires NumPy: http://scipy.org/iRR/R(R2R3RRR4RRtlinalgteigtTtargsortR9tflattentrealR;RRtziptmap( RRRRR=R/R>t eigenvaluest eigenvectorstindtlargesttnormt centrality((sf/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/link_analysis/pagerank_alg.pyRÖs"5    ,"gíµ ÷Æ°>cCs]yddl}Wntk r/tdƒ‚nXt|ƒdkrFiS|dkra|jƒ}n |jƒ}tj|d|d|ddƒ}|j\} } |j |j d d ƒƒj ƒ} d | | dk| | dk<|j j | jdd d |jŒ} | |}|j| ƒ| } |j |j|j d d ƒdkd | dƒƒj ƒ}|dk r—|j t|jƒƒdtƒ}||j ƒ}n| }d}xŸ||krD| }|| ||j||ƒd ||} | | j ƒ} |j| |ƒj ƒ}|| |kr7tt|tt| ƒƒƒS|d 7}q¦Wtd|d ƒ‚dS(sœReturn the PageRank of the nodes in the graph. PageRank computes a ranking of the nodes in the graph G based on the structure of the incoming links. It was originally designed as an algorithm to rank web pages. Parameters ----------- G : graph A NetworkX graph alpha : float, optional Damping parameter for PageRank, default=0.85 personalization: dict, optional The "personalization vector" consisting of a dictionary with a key for every graph node and nonzero personalization value for each node. max_iter : integer, optional Maximum number of iterations in power method eigenvalue solver. tol : float, optional Error tolerance used to check convergence in power method solver. weight : key, optional Edge data key to use as weight. If None weights are set to 1. Returns ------- pagerank : dictionary Dictionary of nodes with PageRank as value Examples -------- >>> G=nx.DiGraph(nx.path_graph(4)) >>> pr=nx.pagerank_scipy(G,alpha=0.9) Notes ----- The eigenvector calculation uses power iteration with a SciPy sparse matrix representation. See Also -------- pagerank, pagerank_numpy, google_matrix References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry, The PageRank citation ranking: Bringing order to the Web. 1999 http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf iÿÿÿÿNs2pagerank_scipy() requires SciPy: http://scipy.org/iR/RR1tfR0igð?tformattcsrsCpagerank_scipy: power iteration failed to convergein %d iterations.(t scipy.sparseR3RRR4RR tto_scipy_sparse_matrixR6R9RRItsparsetspdiagsRGR8R7R:RR;tdottabsoluteRRKRLR(RRRR R!RtscipyR/R>RR?tStQR&R*RCR+RR.((sf/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/link_analysis/pagerank_alg.pyR"s@9   !!$ : !*cCs`ddlm}yddl}Wn|dƒ‚nXyddl}Wn|dƒ‚nXdS(Niÿÿÿÿ(tSkipTestsNumPy not availablesSciPy not available(tnoseR_R2R\(tmoduleR_R2R\((sf/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/link_analysis/pagerank_alg.pyt setup_module†s( t__doc__tnetworkxR tnetworkx.exceptionRt __author__t__all__RRRRRRb(((sf/Users/dxp/prism/prism-games/prism-examples/smgs/car/networkx/algorithms/link_analysis/pagerank_alg.pyts …ALc