This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

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 authority and hub centralities satisfy and . »
  • 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:
In[1]:=
Click for copyable input
Out[1]=
 
HITS hub and authority centralities for a directed graph:
In[1]:=
Click for copyable input
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 :
New in 8