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Average Disorder Number

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The average disorder number of a simple connected graph on n vertices is defined as the average length of a walk along the edges of the graph taken over all ordering of its vertices from 1 to n (Fried 2022).

The average disorder number A(G) is related to the Wiener index W(G) of a graph G with vertex count |G| by

A(G)=(2W(G))/(|G|)

(Fried 2022).

See also

Disorder Number, Walk, Wiener Index

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References

Fried, S. "The Disorder Number of a Graph." 7 Aug 2022. https://arxiv.org/abs/2208.03788/.

Cite this as:

Weisstein, Eric W. "Average Disorder Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AverageDisorderNumber.html

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