GraphLinkEfficiency

GraphLinkEfficiency[g]

gives the link efficiency of the graph g.

GraphLinkEfficiency[{vw,…}]

uses rules vw to specify the graph g.

Details

Examples

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Basic Examples  (2)

Find the link efficiency in the graph:

Graph link efficiency distribution of the Watts–Strogatz graph model:

Scope  (4)

GraphLinkEfficiency works with undirected graphs:

Directed graphs:

Use rules to specify the graph:

GraphLinkEfficiency works with large graphs:

Applications  (2)

Find how tightly connected the overground line of the London Underground is with respect to the number of lines between stations:

Analyze the distribution of link efficiency in the Watts–Strogatz graph model:

Distribution of link efficiency:

Expected value:

Properties & Relations  (5)

GraphLinkEfficiency is related to MeanGraphDistance:

The GraphLinkEfficiency is always less than 1:

The GraphLinkEfficiency of a complete graph is close to 1:

Test if a graph is complete using CompleteGraphQ:

The GraphLinkEfficiency of a path graph of length 1 is 0:

The GraphLinkEfficiency of a disconnected graph is -∞:

Use ConnectedGraphQ to test for connected graphs:

Possible Issues  (1)

Self-loops are ignored:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_graphlinkefficiency, author="Wolfram Research", title="{GraphLinkEfficiency}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/GraphLinkEfficiency.html}", note=[Accessed: 18-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_graphlinkefficiency, organization={Wolfram Research}, title={GraphLinkEfficiency}, year={2015}, url={https://reference.wolfram.com/language/ref/GraphLinkEfficiency.html}, note=[Accessed: 18-November-2024 ]}