Returns HITS hubs and authorities values for nodes.
Deprecated since version 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.
A NetworkX graph
Normalize results by the sum of all of the values.
Two dictionaries keyed by node containing the hub and authority
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.
A. Langville and C. Meyer,
“A survey of eigenvector methods of web information retrieval.”
Authoritative sources in a hyperlinked environment
Journal of the ACM 46 (5): 604-32, 1999.
>>> 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
>>> 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)