LocalClusteringCoefficient [g]
gives the list of local clustering coefficients of all vertices in the graph g.
LocalClusteringCoefficient [g,v]
gives the local clustering coefficient of the vertex v in the graph g.
LocalClusteringCoefficient [{vw,…},…]
uses rules vw to specify the graph g.
LocalClusteringCoefficient
LocalClusteringCoefficient [g]
gives the list of local clustering coefficients of all vertices in the graph g.
LocalClusteringCoefficient [g,v]
gives the local clustering coefficient of the vertex v in the graph g.
LocalClusteringCoefficient [{vw,…},…]
uses rules vw to specify the graph g.
Details
- LocalClusteringCoefficient is also known as clustering coefficient.
- The local clustering coefficient of the vertex v is the fraction of pairs of neighbors of v that are connected over all pairs of neighbors of v.
- LocalClusteringCoefficient works with undirected graphs, directed graphs, and multigraphs.
Examples
open all close allBasic Examples (2)
Compute local clustering coefficients:
Highlight:
Distribution of local clustering coefficients in a graph:
Scope (6)
LocalClusteringCoefficient works with undirected graphs:
Directed graphs:
Multigraphs:
Find the local clustering coefficient of a vertex:
Use rules to specify the graph:
LocalClusteringCoefficient works with large graphs:
Applications (2)
Local clustering coefficients of the internet at the level of autonomous systems:
Plot the mean as a function of the vertex degree:
Local clustering coefficients of Zachary's Karate Club:
Highlight vertices based on their local clustering coefficients:
Properties & Relations (4)
The local clustering coefficients take values between 0 and 1:
The local clustering coefficient of a vertex with less than two neighbors is 0:
All local clustering coefficients of a complete graph with at least three vertices are 1:
MeanClusteringCoefficient gives the mean of LocalClusteringCoefficient :
Related Guides
Text
Wolfram Research (2012), LocalClusteringCoefficient, Wolfram Language function, https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html (updated 2015).
CMS
Wolfram Language. 2012. "LocalClusteringCoefficient." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html.
APA
Wolfram Language. (2012). LocalClusteringCoefficient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html
BibTeX
@misc{reference.wolfram_2025_localclusteringcoefficient, author="Wolfram Research", title="{LocalClusteringCoefficient}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html}", note=[Accessed: 17-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_localclusteringcoefficient, organization={Wolfram Research}, title={LocalClusteringCoefficient}, year={2015}, url={https://reference.wolfram.com/language/ref/LocalClusteringCoefficient.html}, note=[Accessed: 17-November-2025]}