gives the link efficiency of the graph g.

uses rules vw to specify the graph g.

# Details

• GraphLinkEfficiency is also known as global efficiency or efficiency.
• Measures how tightly connected the graph g is in relation to its number of edges.
• uses the underlying simple graph of g. For a simple unweighted graph, is given by 1-MeanGraphDistance[g]/EdgeCount[g].

# 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)

Directed graphs:

Use rules to specify the graph:

## 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:

Expected value:

## Properties & Relations(5)

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: