o 3ήcq.@sTdZddlZgdZdddZdd d Zdd d Zdd dZdddZdddZ dS)z2Hubs and authorities analysis of graph structure. N)hits hits_numpy hits_scipyauthority_matrix hub_matrixd:0yE>TcCsddl}ddl}ddl}t|dkriifStj|t|td}|dur3|jj j |d||d\} } } n| t| }|jj j |d|||d\} } } | j} || } |rb| | } | | } tt|tt| } tt|tt| }| |fS)aReturns HITS hubs and authorities values for nodes. The HITS algorithm computes two numbers for a node. Authorities estimates the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Parameters ---------- G : graph A NetworkX graph max_iter : integer, optional Maximum number of iterations in power method. tol : float, optional Error tolerance used to check convergence in power method iteration. nstart : dictionary, optional Starting value of each node for power method iteration. normalized : bool (default=True) Normalize results by the sum of all of the values. Returns ------- (hubs,authorities) : two-tuple of dictionaries Two dictionaries keyed by node containing the hub and authority values. Raises ------ PowerIterationFailedConvergence If the algorithm fails to converge to the specified tolerance within the specified number of iterations of the power iteration method. Examples -------- >>> G = nx.path_graph(4) >>> h, a = nx.hits(G) 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 HITS algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs. References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-32, 1999. doi:10.1145/324133.324140. http://www.cs.cornell.edu/home/kleinber/auth.pdf. rN)nodelistdtype)kmaxitertol)r v0r r)numpyscipyscipy.sparse.linalglennxadjacency_matrixlistfloatsparselinalgsvdsarrayvaluesflattenrealsumdictzipmap)Gmax_iterrnstart normalizednpsprA_vtahhubs authoritiesr0Q/tmp/pip-target-vg8gfxp4/lib/python/networkx/algorithms/link_analysis/hits_alg.pyrs$@    rc st|tjtjfr tdt|dkriifS|dur&t|d|n|dt }D] }||9<q2t |D]}t dt d}D]} || D]} || | || |  dd7<q]qWD]} || D]} | || || |  dd7<q}qwdt }D] } | |9<qdt| }|D] } || |9<qt fddD} | |krnqAt||rdt | }|D] } || |9<qdt }D] } | |9<q|fS)Nz.hits() not defined for graphs with multiedges.rg?weightr c3s$|] }t||VqdSN)abs.0nr-hlastr0r1 s"z_hits_python..) isinstancer MultiGraph MultiDiGraph Exceptionrr fromkeysnumber_of_nodesrrrangekeysgetmaxPowerIterationFailedConvergence) r#r$rr%r&sr r*r,r7nbrerrr0r8r1 _hits_python`sR   * * rIcCs0ddl}d}||ttj||d}|j|S)z@Returns the HITS authority matrix. .. deprecated:: 2.6 rNz authority_matrix is deprecated as of version 2.6 and will be removed in version 3.0. The authority matrix can be computed by:: >>> M = nx.to_numpy_array(G, nodelist=nodelist) >>> M.T @ Mr warningswarnDeprecationWarningrto_numpy_arrayTr#r rLmsgMr0r0r1r   rcCs0ddl}d}||ttj||d}||jS)z:Returns the HITS hub matrix. .. deprecated:: 2.6 rNz hub_matrix is deprecated as of version 2.6 and will be removed in version 3.0. The hub matrix can be computed by:: >>> M = nx.to_numpy_array(G, nodelist=nodelist) >>> M @ M.TrJrKrQr0r0r1rrTrc Csddl}ddl}|jdtddt|dkriifSt|}||j}|j |\}}|dd| |f}|j|} |j | \}}|dd| |f} |r^|| }| | } n || }| | } t t|tt|} t t|tt| } | | fS)aReturns HITS hubs and authorities values for nodes. .. deprecated:: 2.6 hits_numpy is deprecated and will be removed in networkx 3.0. The HITS algorithm computes two numbers for a node. Authorities estimates the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Parameters ---------- G : graph A NetworkX graph normalized : bool (default=True) Normalize results by the sum of all of the values. Returns ------- (hubs,authorities) : two-tuple of dictionaries Two dictionaries keyed by node containing the hub and authority values. Examples -------- >>> G = nx.path_graph(4) The `hubs` and `authorities` are given by the eigenvectors corresponding to the maximum eigenvalues of the hubs_matrix and the authority_matrix, respectively. The ``hubs`` and ``authority`` matrices are computed from the adjancency matrix: >>> adj_ary = nx.to_numpy_array(G) >>> hubs_matrix = adj_ary @ adj_ary.T >>> authority_matrix = adj_ary.T @ adj_ary `hits_numpy` maps the eigenvector corresponding to the maximum eigenvalue of the respective matrices to the nodes in `G`: >>> hubs, authority = nx.hits_numpy(G) Notes ----- The eigenvector calculation uses NumPy's interface to LAPACK. The HITS algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs. References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-32, 1999. doi:10.1145/324133.324140. http://www.cs.cornell.edu/home/kleinber/auth.pdf. rNz`networkx.hits_numpy is deprecated and will be removedin NetworkX 3.0, use networkx.hits instead. stacklevel)rLrrMrNrrrOrPreigargmaxrrDr r!r"r) r#r&rLr'adj_aryHeevr-r)r,r.r/r0r0r1rs0?       rư>csTddl}ddl}|jdtddt|dkriifStj|t|d}|j\}} |j |} dur;| |df|} n|j fdd t|Dt d } | | } d} | } | | } | | } || |  }||krnn| |krwt|| d7} qT| }||}|r|| }|| }tt|tt |}tt|tt |}||fS) aYReturns HITS hubs and authorities values for nodes. .. deprecated:: 2.6 hits_scipy is deprecated and will be removed in networkx 3.0 The HITS algorithm computes two numbers for a node. Authorities estimates the node value based on the incoming links. Hubs estimates the node value based on outgoing links. Parameters ---------- G : graph A NetworkX graph max_iter : integer, optional Maximum number of iterations in power method. tol : float, optional Error tolerance used to check convergence in power method iteration. nstart : dictionary, optional Starting value of each node for power method iteration. normalized : bool (default=True) Normalize results by the sum of all of the values. Returns ------- (hubs,authorities) : two-tuple of dictionaries Two dictionaries keyed by node containing the hub and authority values. Examples -------- >>> G = nx.path_graph(4) >>> h, a = nx.hits(G) Notes ----- This implementation uses SciPy sparse matrices. 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 HITS algorithm was designed for directed graphs but this algorithm does not check if the input graph is directed and will execute on undirected graphs. Raises ------ PowerIterationFailedConvergence If the algorithm fails to converge to the specified tolerance within the specified number of iterations of the power iteration method. References ---------- .. [1] A. Langville and C. Meyer, "A survey of eigenvector methods of web information retrieval." http://citeseer.ist.psu.edu/713792.html .. [2] Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-632, 1999. doi:10.1145/324133.324140. http://www.cs.cornell.edu/home/kleinber/auth.pdf. rNz`networkx.hits_scipy is deprecated and will be removedin NetworkX 3.0, use networkx.hits instead.rUrVrJr csg|]}|dqS)r)rCr5r%r0r1 wszhits_scipy..)r )rLrrMrNrrto_scipy_sparse_arrayrshaperPonesrrrrDabsoluterErr r!r")r#r$rr%r&rLr'r)r7r*ATAxixlastrHr,r-r.r/r0r_r1rsHF          r)rrNTr3)T)rr^NT) __doc__networkxr__all__rrIrrrrr0r0r0r1s  X 3  b