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HITSCentrality

HITSCentrality

HITSCentrality[g]

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

HITSCentrality[{vw,…}]

uses rules vw to specify the graph g.

Details and Options

HITSCentrality is also known as Kleinberg centrality.
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 , 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:

CompleteKaryTree:

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:

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