As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »


gives the link ranks of the directed graph g as a rule list.

Details and Options

  • LinkRanks functionality is now available in the built-in Wolfram Language function LinkRankCentrality.
  • To use LinkRanks, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
  • The following options can be given:
  • ToleranceAutomatictolerance used for convergence check
    TeleportProbability0.15probability of visiting random nodes
    RemoveSinksTruewhether to remove sinks by linking them with every node
  • The link rank of a link from vertex i to vertex j is defined as page rank of i, as given by PageRanks[g], divided by the out-degree of i.
  • The link rank reflects the probability that a random surfer follows that link.
  • LinkRanks has the same options as PageRanks.


Basic Examples  (2)

This defines a small directed graph:

This calculates the link ranks:

LinkRanks has been superseded by LinkRankCentrality:

Wolfram Research (2007), LinkRanks, Wolfram Language function,


Wolfram Research (2007), LinkRanks, Wolfram Language function,


Wolfram Language. 2007. "LinkRanks." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2007). LinkRanks. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_linkranks, author="Wolfram Research", title="{LinkRanks}", year="2007", howpublished="\url{}", note=[Accessed: 15-June-2024 ]}


@online{reference.wolfram_2024_linkranks, organization={Wolfram Research}, title={LinkRanks}, year={2007}, url={}, note=[Accessed: 15-June-2024 ]}