hits

hits(G, max_iter=100, tol=1e-08, nstart=None, normalized=True, *, method='power_iteration')

Returns 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:

Ggraph

A NetworkX graph

max_iterinteger, optional

Maximum number of iterations in power method.

tolfloat, optional

Error tolerance used to check convergence in power method iteration.

nstartdictionary, optional

Starting value of each node for power method iteration.

normalizedbool (default=True)

Normalize results by the sum of all of the values.

methodstring (default=”power_iteration”)

The implementation to use, one of “power_iteration” or “svd”. The “svd” method computes the values from the largest singular value/vectors of the adjacency matrix using scipy.sparse.linalg.svds.

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.

ValueError

If method is not one of “power_iteration” or “svd”.

Notes

With method="power_iteration", 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 when the change in the hub values between two successive iterations is smaller than tol. With method="svd", max_iter and tol are passed to scipy.sparse.linalg.svds.

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.” https://epubs.siam.org/doi/epdf/10.1137/S0036144503424786

[2]

Jon Kleinberg, Authoritative sources in a hyperlinked environment Journal of the ACM 46 (5): 604-32, 1999. https://www.cs.cornell.edu/home/kleinber/auth.pdf doi:10.1145/324133.324140.

Examples

>>> G = nx.path_graph(4)
>>> h, a = nx.hits(G)

Additional backends implement this function

cugraphGPU-accelerated backend.

Additional parameters:

dtypedtype or None, optional

The data type (np.float32, np.float64, or None) to use for the edge weights in the algorithm. If None, then dtype is determined by the edge values.

weightstring or None, optional (default=”weight”)

The edge attribute to use as the edge weight.

graphblas : OpenMP-enabled sparse linear algebra backend.