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LinkRanks

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

LinkRanks[g]

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.

Examples

Basic Examples  (2)Summary of the most common use cases

In[1]:=1
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https://wolfram.com/xid/0wbwdnkb9g-cfx6cl

This defines a small directed graph:

In[2]:=2
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https://wolfram.com/xid/0wbwdnkb9g-1d3kao

This calculates the link ranks:

In[3]:=3
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https://wolfram.com/xid/0wbwdnkb9g-pkhc0i
Out[3]=3

LinkRanks has been superseded by LinkRankCentrality:

In[1]:=1
✖
https://wolfram.com/xid/0wbwdnkb9g-hi209b
In[2]:=2
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https://wolfram.com/xid/0wbwdnkb9g-dlnrwm
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0wbwdnkb9g-fbil3c
Out[3]=3
Wolfram Research (2007), LinkRanks, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html.
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Wolfram Research (2007), LinkRanks, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html.

Text

Wolfram Research (2007), LinkRanks, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html.

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Wolfram Research (2007), LinkRanks, Wolfram Language function, https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html.

CMS

Wolfram Language. 2007. "LinkRanks." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html.

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Wolfram Language. 2007. "LinkRanks." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html.

APA

Wolfram Language. (2007). LinkRanks. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html

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Wolfram Language. (2007). LinkRanks. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html

BibTeX

@misc{reference.wolfram_2025_linkranks, author="Wolfram Research", title="{LinkRanks}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html}", note=[Accessed: 08-July-2025 ]}

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@misc{reference.wolfram_2025_linkranks, author="Wolfram Research", title="{LinkRanks}", year="2007", howpublished="\url{https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html}", note=[Accessed: 08-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_linkranks, organization={Wolfram Research}, title={LinkRanks}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html}, note=[Accessed: 08-July-2025 ]}

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@online{reference.wolfram_2025_linkranks, organization={Wolfram Research}, title={LinkRanks}, year={2007}, url={https://reference.wolfram.com/language/GraphUtilities/ref/LinkRanks.html}, note=[Accessed: 08-July-2025 ]}