HITSCentrality

HITSCentrality[g]

gives a list of authority and hub centralities for the vertices in the graph g.

HITSCentrality[{vw,}]

uses rules vw to specify the graph g.

Details and Options

  • HITSCentrality gives two lists of authority centralities and hub centralities for each vertex.
  • If the graph g has adjacency matrix , then authority centralities are given by TemplateBox[{a}, Transpose].a.x=lambda_1 x, where is the largest eigenvalue of TemplateBox[{a}, Transpose].a, and hub centralities are given by . »
  • The authority and hub centralities satisfy and x=1/lambda_1TemplateBox[{a}, Transpose].y. »
  • The option WorkingPrecision->p can be used to control the precision used in internal computations.
  • HITSCentrality works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (2)

Compute HITS hub and authority centralities:

Chart of the data:

Rate web pages using hyperlink-induced topic search:

Web pages with high hub centralities are connected to many other web pages:

Web pages with high authority centralities are connected from many other web pages:

Scope  (6)

HITSCentrality works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

HITSCentrality works with large graphs:

Options  (3)

WorkingPrecision  (3)

By default, HITSCentrality finds centralities using machine-precision computations:

Specify a higher working precision:

Infinite working precision corresponds to exact computation:

Applications  (3)

Highlight the HITS authority and hub centralities for CycleGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

A network of web pages linked via hyperlinks. Find the top five informative web pages:

Find the top five pages containing authoritative information:

HITS authority ranking is highly correlated with in-degree ranking:

Find the top five pages containing links to authoritative pages:

HITS hub ranking is highly correlated with out-degree ranking:

Properties & Relations  (4)

The authority and hub centrality can be found using the first eigenvector of :

Authority centrality:

Hub centrality:

The authority and hub centralities satisfy and x=TemplateBox[{{{1, /, {lambda, _, 1}}, a}}, Transpose].y:

The authority centrality is normalized:

Use VertexIndex to obtain the authority centrality and hub centrality of a specific vertex:

Introduced in 2010
 (8.0)
 |
Updated in 2014
 (10.0)
2015
 (10.3)