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LinkRankCentrality
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LinkRankCentrality

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

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

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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

open allclose all

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

Compute link-rank centralities:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-dprrh4
In[2]:=2
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https://wolfram.com/xid/0v51t46a4r4ou-3cvhh
Out[2]=2

Highlight:

In[3]:=3
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https://wolfram.com/xid/0v51t46a4r4ou-g4cic3
In[4]:=4
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https://wolfram.com/xid/0v51t46a4r4ou-dqn9rm
Out[4]=4

Find the probability that a random surfer follows that link:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-hep6lg
In[2]:=2
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https://wolfram.com/xid/0v51t46a4r4ou-jtwb18
Out[2]=2

Rank web links, with the most visible links first:

In[3]:=3
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https://wolfram.com/xid/0v51t46a4r4ou-bxg7c3

Scope  (7)Survey of the scope of standard use cases

LinkRankCentrality works with undirected graphs:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-bwkmje
Out[1]=1

Directed graphs:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-bgzrn4
Out[1]=1

Multigraphs:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-ikyy8
Out[1]=1

Mixed graphs:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-czvddh
Out[1]=1

Use rules to specify the graph:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-bndh30
Out[1]=1

Nondefault initial centralities:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-coe4mi
Out[1]=1

LinkRankCentrality works with large graphs:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-pq9ae
In[2]:=2
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https://wolfram.com/xid/0v51t46a4r4ou-cevvx1
Out[2]=2

Options  (3)Common values & functionality for each option

WorkingPrecision  (3)

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

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-bg8b8
Out[1]=1

Specify a higher working precision:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-e6isci
Out[1]=1

Infinite working precision corresponds to exact computation:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-jsrmu
Out[1]=1

Applications  (2)Sample problems that can be solved with this function

Highlight the link-rank centrality for CycleGraph:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-blvy5f
In[2]:=2
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https://wolfram.com/xid/0v51t46a4r4ou-baipzx
In[3]:=3
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https://wolfram.com/xid/0v51t46a4r4ou-g2btke
In[4]:=4
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https://wolfram.com/xid/0v51t46a4r4ou-h351s2
Out[4]=4

GridGraph:

In[5]:=5
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https://wolfram.com/xid/0v51t46a4r4ou-jbz7i6
In[6]:=6
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https://wolfram.com/xid/0v51t46a4r4ou-brg6kn
In[7]:=7
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https://wolfram.com/xid/0v51t46a4r4ou-hyiutu
Out[7]=7

CompleteKaryTree:

In[8]:=8
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https://wolfram.com/xid/0v51t46a4r4ou-gca8u7
In[9]:=9
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https://wolfram.com/xid/0v51t46a4r4ou-gcylrp
In[10]:=10
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https://wolfram.com/xid/0v51t46a4r4ou-bp9wqg
Out[10]=10

PathGraph:

In[11]:=11
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https://wolfram.com/xid/0v51t46a4r4ou-6ri66
In[12]:=12
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https://wolfram.com/xid/0v51t46a4r4ou-fh33ql
In[13]:=13
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https://wolfram.com/xid/0v51t46a4r4ou-iop80
Out[13]=13

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

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-etjd7f
In[2]:=2
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https://wolfram.com/xid/0v51t46a4r4ou-fa6bgl
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

LinkRankCentrality can be found using PageRankCentrality:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-fuqhxf
Out[1]=1
In[4]:=4
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https://wolfram.com/xid/0v51t46a4r4ou-hfzr3e
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0v51t46a4r4ou-eo966g
Out[5]=5

Use EdgeIndex to obtain the centrality of a specific vertex:

In[1]:=1
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https://wolfram.com/xid/0v51t46a4r4ou-szwpd
In[2]:=2
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https://wolfram.com/xid/0v51t46a4r4ou-bbshqt
Out[2]=2
Wolfram Research (2014), LinkRankCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/LinkRankCentrality.html (updated 2015).
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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).

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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.

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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

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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: 11-May-2025 ]}

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@misc{reference.wolfram_2025_linkrankcentrality, author="Wolfram Research", title="{LinkRankCentrality}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LinkRankCentrality.html}", note=[Accessed: 11-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: 11-May-2025 ]}

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@online{reference.wolfram_2025_linkrankcentrality, organization={Wolfram Research}, title={LinkRankCentrality}, year={2015}, url={https://reference.wolfram.com/language/ref/LinkRankCentrality.html}, note=[Accessed: 11-May-2025 ]}