gives the link efficiency of the graph g.
uses rules vw to specify the graph g.
- GraphLinkEfficiency is also known as global efficiency or efficiency.
- Measures how tightly connected the graph g is in relation to its number of edges.
- GraphLinkEfficiency[g] uses the underlying simple graph of g. For a simple unweighted graph, GraphLinkEfficiency[g] is given by 1-MeanGraphDistance[g]/EdgeCount[g].
Examplesopen allclose all
Basic Examples (2)
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:
Wolfram Research (2012), GraphLinkEfficiency, Wolfram Language function, https://reference.wolfram.com/language/ref/GraphLinkEfficiency.html (updated 2015).
Wolfram Language. 2012. "GraphLinkEfficiency." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/GraphLinkEfficiency.html.
Wolfram Language. (2012). GraphLinkEfficiency. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GraphLinkEfficiency.html