BUILT-IN MATHEMATICA SYMBOL

HITSCentrality

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

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 where is the largest eigenvalue of and hub centralities are given by . »

The option WorkingPrecision->p can be used to control precision used in internal computations.

HITS hub and authority centralities for an undirected graph:

HITS hub and authority centralities for a directed graph:

HITS hub and authority centralities for an undirected graph:

Out[1]=

HITS hub and authority centralities for a directed graph:

Out[1]=

HITSCentrality for undirected graphs:

Directed graphs:

Label the vertex with in-degree and out-degree:

Highlight the authority centrality:

Highlight the hub centrality:

Work with large graphs:

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

Specify a higher working precision:

Infinite working precision corresponds to exact computation:

Highlight the HITS authority and hub centralities for CycleGraph:

An unbalanced tree:

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

:

Authority centrality:

Hub centrality:

The authority

and hub

centralities satisfy

and

: