LinkRankCentrality

LinkRankCentrality[g,α]

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

LinkRankCentrality[g,α,β]

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

LinkRankCentrality[{vw,…},…]

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.

Examples

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Basic Examples  (2)

Compute link-rank centralities:

Highlight:

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:

Multigraphs:

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:

GridGraph:

CompleteKaryTree:

PathGraph:

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, https://reference.wolfram.com/language/ref/LinkRankCentrality.html (updated 2015).

Text

Wolfram Research (2014), LinkRankCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/LinkRankCentrality.html (updated 2015).

CMS

Wolfram Language. 2014. "LinkRankCentrality." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/LinkRankCentrality.html.

APA

Wolfram Language. (2014). LinkRankCentrality. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinkRankCentrality.html

BibTeX

@misc{reference.wolfram_2025_linkrankcentrality, author="Wolfram Research", title="{LinkRankCentrality}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LinkRankCentrality.html}", note=[Accessed: 09-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_linkrankcentrality, organization={Wolfram Research}, title={LinkRankCentrality}, year={2015}, url={https://reference.wolfram.com/language/ref/LinkRankCentrality.html}, note=[Accessed: 09-May-2025 ]}