Vh(jdZddlZdgZejdddiid dZd d Zd d Zdd Zy)z1Hubs and authorities analysis of graph structure.NhitsGweight)preserve_edge_attrsc  ddl}ddl}t|dk(riifStj|t |t }|(|jt |j}|dkrtj| |jjj|d|||\}}} | jj} || z} |r&| | j!z} | | j!z} t#t%|t't | } t#t%|t't | }| |fS#|jjj$r} tj|| d} ~ wwxYw)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)nodelistdtyper)kv0maxitertol)numpyscipylennxadjacency_matrixlistfloatarrayvaluesPowerIterationFailedConvergencesparselinalgsvdsArpackNoConvergenceflattenrealsumdictzipmap)rmax_iterrnstart normalizednpspA_vtexcahhubs authoritiess Z/home/dcms/DCMS/lib/python3.12/site-packages/networkx/algorithms/link_analysis/hits_alg.pyrrsMB 1v{2v  AQu=A $v}}/01}00::D99##((aFHRU(V1b A AA QUUW  QUUW  As5!}% &Ds1c%m,-K   99   / /D00:CDs.E#F'E==Fc  t|tjtjzr t dt |dk(riifS|(t j|d|jz  n2| dt jz } D]} |xx|zcc<t|D]=} t j jd t j jd} D]5} || D]+} || xx | || | jddzz cc<-7 D]5} || D]+} | xx|| || | jddzz cc<-7dt jz } D]} | xx|zcc<dt|jz }|D]} || xx|zcc<t fd D} | |ks>ntj||r`dt|jz }|D]} || xx|zcc<dt jz } D]} | xx|zcc< |fS)Nz.hits() not defined for graphs with multiedges.rg?rrc3FK|]}t||z yw)N)abs).0nr-hlasts r0 z_hits_python..s"21#adU1Xo&2s!) isinstancer MultiGraph MultiDiGraph Exceptionrr fromkeysnumber_of_nodesrrrangekeysgetmaxr)rr#rr$r%sr r)r,r5nbrerrr-r6s @@r0 _hits_pythonrEcsu!R]]R__45HII 1v{2v  ~ MM!S1#4#4#66 7  #ahhj/ ! A aDAID  8_; MM%**, * MM%**, * @At @#%(QqT#Y]]8Q%??? @ @ >> 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 adjacency 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`: >>> from networkx.algorithms.link_analysis.hits_alg import _hits_numpy >>> hubs, authority = _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. rN)rrrto_numpy_arrayTreigargmaxrrAr r!r"r) rr%r&adj_aryHeevr-r(r,r.r/s r0 _hits_numpyrPsx 1v{2v "G'))A IIMM! EAr 1biil?A GA IIMM! EAr 1biil?A QUUW  QUUW  QUUW  QUUW  As5!}% &Ds1c%m,-K  rFc `ddl}t|dk(riifStj|t |}|j \}}|j |z} ||j|df|z } nQ|jt |Dcgc]}|j|dc}t} | | jz} d} | } | | z} | | jz} |j| | z j} | |krn | |kDrtj|| dz } b| j}||z}|r&||jz}||jz}t!t#|t%t|}t!t#|t%t|}||fScc}w)aKReturns 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. Examples -------- >>> from networkx.algorithms.link_analysis.hits_alg import _hits_scipy >>> G = nx.path_graph(4) >>> h, a = _hits_scipy(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. rN)r r)r )rrrto_scipy_sparse_arrayrshaperIonesrr@rrrAabsoluterrr r!r")rr#rr$r%r&r(r5r)ATAxixlastrDr,r-r.r/s r0 _hits_scipyrZsH 1v{2v    T!W5A WWFQ ##'C ~ GGQFOa  HHQ81fjjA&8H F QUUW  A  !G QUUW kk!e)$((* 9  x<44X> > Q  A AA QUUW  QUUW  As5!}% &Ds1c%m,-K  19sF+)dg:0yE>NT)T)r[gư>NT) __doc__networkxr__all__ _dispatchablerrErPrZrFr0rasR7 (sXqM&:;W<Wt0fQhgrF