MeanDegreeConnectivity

MeanDegreeConnectivity[g]

gives a list of k-mean degree connectivity for the graph g for successive k=0,1,2… .

MeanDegreeConnectivity[g,"In"]

gives a list of k-mean in-degree connectivity for the graph g.

MeanDegreeConnectivity[g,"Out"]

gives a list of k-mean out-degree connectivity for the graph g.

MeanDegreeConnectivity[{vw,…},…]

uses rules vw to specify the graph g.

Details

  • The mean degree connectivity is also known as average degree connectivity and average nearest neighbor degree.
  • The k-mean degree connectivity is the average of the mean neighbor degrees of vertices of degree k.
  • MeanDegreeConnectivity[g] returns a list {m0,m1,…,md}, where mk is the k-mean degree connectivity and d is the maximum vertex degree in g.
  • MeanDegreeConnectivity works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

open allclose all

Basic Examples  (2)

Compute the mean degree connectivity for a graph:

Plot the mean degree connectivity:

Scope  (8)

MeanDegreeConnectivity works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Compute the mean in- and out-degree connectivity:

MeanDegreeConnectivity works with large graphs:

Properties & Relations  (1)

MeanDegreeConnectivity[g][[k+1]] gives the k-mean degree connectivity:

It is a mean of MeanNeighborDegree:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_meandegreeconnectivity, author="Wolfram Research", title="{MeanDegreeConnectivity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/MeanDegreeConnectivity.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_meandegreeconnectivity, organization={Wolfram Research}, title={MeanDegreeConnectivity}, year={2015}, url={https://reference.wolfram.com/language/ref/MeanDegreeConnectivity.html}, note=[Accessed: 21-December-2024 ]}