gives a list of authority and hub centralities for the vertices in 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 , where is the largest eigenvalue of , and hub centralities are given by . »
- The authority and hub centralities satisfy and . »
- 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.
Examplesopen allclose all
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:
HITSCentrality works with undirected graphs:
Use rules to specify the graph:
HITSCentrality works 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:
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 :
The authority and hub centralities satisfy and :
The authority centrality is normalized:
Use VertexIndex to obtain the authority centrality and hub centrality of a specific vertex:
Introduced in 2010
Updated in 2014