WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

MeanClusteringCoefficient
✖
MeanClusteringCoefficient

✖

gives the mean clustering coefficient of the graph g.

✖

uses rules vw to specify the graph g.

Details

  • MeanClusteringCoefficient is also known as the average or overall clustering coefficient.
  • The mean clustering coefficient of g is the mean over all local clustering coefficients of vertices of g.
  • MeanClusteringCoefficient works with undirected graphs, directed graphs, and multigraphs.

Examples

open allclose all

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

Find the mean clustering coefficient of a graph:

In[3]:=3
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-ufoiod
Out[3]=3

Mean clustering coefficient in the Watts–Strogatz model as a function of rewiring probability:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-rtcihx
Out[1]=1

Scope  (5)Survey of the scope of standard use cases

MeanClusteringCoefficient works with undirected graphs:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-s1xzj6
Out[1]=1

Directed graphs:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-m7dj72
Out[1]=1

Multigraphs:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-15kl6n
Out[1]=1

Use rules to specify the graph:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-bndh30
Out[1]=1

MeanClusteringCoefficient works with large graphs:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-cddhqp
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-ycsczv
Out[2]=2

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

Mean clustering coefficient of a power grid network:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-nsiejz
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-us382s
Out[2]=2

Compare to uniform random graphs:

In[3]:=3
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-9kkcjs
In[4]:=4
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-hcvghy
Out[4]=4

Collaboration networks tend to have high mean clustering coefficients:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-uu9rv1
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-q76y9z
Out[2]=2

Compare to uniform random graphs:

In[3]:=3
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-maobl4
In[4]:=4
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-5z0tcr
Out[4]=4

Properties & Relations  (7)Properties of the function, and connections to other functions

MeanClusteringCoefficient is the mean over all local clustering coefficients of vertices:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-826kjq
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-ic3p1b
Out[2]=2

The mean clustering coefficient is between 0 and 1:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-w1hdto
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-zrslmi
Out[2]=2

For a graph with no vertices of degree greater than 1, the mean clustering coefficient is 0:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-0zinzo
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-g2qcfc
Out[2]=2

The mean clustering coefficient of a complete graph with at least three vertices is 1:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-6rjps4
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-nis1k1
Out[2]=2

Distribution of mean clustering coefficient in BernoulliGraphDistribution:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-ij59gx
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-2wa8us
Out[2]=2

Expected value:

In[3]:=3
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-7e39kr
Out[3]=3

Distribution of mean clustering coefficient in WattsStrogatzGraphDistribution:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-hsxdys
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-xwz21h
Out[2]=2

With low rewiring probability and high mean vertex degree, the expected value is near :

In[3]:=3
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-0qub8l
Out[3]=3

With high rewiring probability, the expected value is near 0:

In[4]:=4
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-mw85vu
Out[4]=4

Distribution of mean clustering coefficient in BarabasiAlbertGraphDistribution:

In[1]:=1
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-c5r7d
In[2]:=2
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-kafjru
In[3]:=3
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-w49qs5
Out[3]=3

Compare with GlobalClusteringCoefficient:

In[4]:=4
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-t3y2qh
In[5]:=5
✖
https://wolfram.com/xid/08ud9k0mn4dgui6-w928v8
Out[5]=5
Wolfram Research (2012), MeanClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html (updated 2015).
✖
Wolfram Research (2012), MeanClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html (updated 2015).

Text

Wolfram Research (2012), MeanClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html (updated 2015).

✖
Wolfram Research (2012), MeanClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html (updated 2015).

CMS

Wolfram Language. 2012. "MeanClusteringCoefficient." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html.

✖
Wolfram Language. 2012. "MeanClusteringCoefficient." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html.

APA

Wolfram Language. (2012). MeanClusteringCoefficient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html

✖
Wolfram Language. (2012). MeanClusteringCoefficient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html

BibTeX

@misc{reference.wolfram_2025_meanclusteringcoefficient, author="Wolfram Research", title="{MeanClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}", note=[Accessed: 26-March-2025 ]}

✖
@misc{reference.wolfram_2025_meanclusteringcoefficient, author="Wolfram Research", title="{MeanClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_meanclusteringcoefficient, organization={Wolfram Research}, title={MeanClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}, note=[Accessed: 26-March-2025 ]}

✖
@online{reference.wolfram_2025_meanclusteringcoefficient, organization={Wolfram Research}, title={MeanClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/MeanClusteringCoefficient.html}, note=[Accessed: 26-March-2025 ]}