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KatzCentrality

KatzCentrality
gives a list of Katz centralities for the vertices in the graph g and weight .
KatzCentrality
gives a list of Katz centralities using weight and initial centralities .
  • KatzCentrality gives a list of centralities that satisfy , where is the adjacency matrix of g.
  • With a scalar, it is taken to mean .
  • With , the centralities are all given by .
  • The option WorkingPrecision->p can be used to control the precision used in internal computations.
Katz centralities for an undirected graph:
With nondefault initial centralities:
Katz centralities for a directed graph:
Katz centralities for an undirected graph:
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With nondefault initial centralities:
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Katz centralities for a directed graph:
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KatzCentrality for undirected graphs:
Directed graphs:
Works with large graphs:
By default, KatzCentrality finds centralities using machine-precision computations:
Specify a higher working precision:
Infinite working precision corresponds to exact computation:
Highlight the Katz centrality for CycleGraph:
An unbalanced tree:
Create a directed graph that represents a citation network:
Find the top 5 most important papers and highlight them:
The centrality vector satisfies the equation :
Use as the parameter for KatzCentrality:
As all vertices get the same centrality:
New in 8