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 WattsStrogatz 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 WattsStrogatz 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:

Introduced in 2012
 (9.0)
 |
Updated in 2015
 (10.3)