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PageRankCentrality

PageRankCentrality
gives a list of page-rank centralities for the vertices in the graph g and weight .
PageRankCentrality
gives a list of page-rank centralities using weight and initial centralities .
  • PageRankCentrality gives a list of centralities that satisfy , where is the adjacency matrix of g and is the diagonal matrix consisting of , where is the out-degree of the ^(th) vertex. »
  • With a scalar it is taken to mean .
  • The option WorkingPrecision->p can be used to control the precision used in internal computations.
Page-rank centralities for an undirected graph:
With nondefault initial centralities:
Page-rank centralities for a directed graph:
Page-rank centralities for an undirected graph:
In[1]:=
Click for copyable input
Out[1]=
With nondefault initial centralities:
In[2]:=
Click for copyable input
Out[2]=
 
Page-rank centralities for a directed graph:
In[1]:=
Click for copyable input
Out[1]=
PageRankCentrality for undirected graphs:
Directed graphs:
Works with large graphs:
By default, PageRankCentrality finds centralities using machine-precision computations:
Specify a higher working precision:
Infinite working precision corresponds to exact computation:
Highlight the page-rank centrality for CycleGraph:
An unbalanced tree:
Create a directed graph which represents a citation network:
Find the top five most important papers and highlight them:
The centrality vector satisfies the equation :
New in 8