gives the link-rank centralities for edges in the graph g and weight α.


gives the link-rank centralities, using weight α and initial vertex page-rank centralities β.


uses rules vw to specify the graph g.

Details and Options

  • Link-rank centralities represent the likelihood that a person randomly follows a particular link on the web graph.
  • Link rank is a way of measuring the importance of links between vertices.
  • The link-rank centrality of an edge is the page-rank centrality of its source vertex, divided by its out-degree.
  • If β is a scalar, it is taken to mean {β,β,}.
  • LinkRankCentrality[g,α] is equivalent to LinkRankCentrality[g,α,1/VertexCount[g]].
  • Link-rank centralities are normalized.
  • The option WorkingPrecision->p can be used to control the precision used in internal computations.
  • LinkRankCentrality works with undirected graphs, directed graphs, multigraphs, and mixed graphs.


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Basic Examples  (2)

Compute link-rank centralities:


Find the probability that a random surfer follows that link:

Rank web links, with the most visible links first:

Scope  (7)

LinkRankCentrality works with undirected graphs:

Directed graphs:


Mixed graphs:

Use rules to specify the graph:

Nondefault initial centralities:

LinkRankCentrality works with large graphs:

Options  (3)

WorkingPrecision  (3)

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

Specify a higher working precision:

Infinite working precision corresponds to exact computation:

Applications  (2)

Highlight the link-rank centrality for CycleGraph:




Rank website links based on the likelihood that a random surfer follows that link:

Properties & Relations  (2)

LinkRankCentrality can be found using PageRankCentrality:

Use EdgeIndex to obtain the centrality of a specific vertex:

Wolfram Research (2014), LinkRankCentrality, Wolfram Language function, (updated 2015).


Wolfram Research (2014), LinkRankCentrality, Wolfram Language function, (updated 2015).


Wolfram Language. 2014. "LinkRankCentrality." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015.


Wolfram Language. (2014). LinkRankCentrality. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_linkrankcentrality, author="Wolfram Research", title="{LinkRankCentrality}", year="2015", howpublished="\url{}", note=[Accessed: 19-July-2024 ]}


@online{reference.wolfram_2024_linkrankcentrality, organization={Wolfram Research}, title={LinkRankCentrality}, year={2015}, url={}, note=[Accessed: 19-July-2024 ]}