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Excess


The kurtosis excess of a distribution is sometimes called the excess, or excess coefficient.

In graph theory, excess refers to the quantity

 e=n-n_l(v,g)
(1)

for a v-regular graph G on n nodes with girth g, where

 n_l(v,g)={(v(v-1)^((g-1)/2)-2)/(v-2)   for g odd; (2(v-1)^(g/2)-2)/(v-2)   for g even
(2)

(Biggs and Ito 1980, Wong 1982). A (v,g)-cage graph having n(v,g)=n_l(v,g) vertices (i.e., the minimal number, so that the excess is e=0) is called a Moore graph.


See also

Cage Graph, Kurtosis, Moore Graph

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References

Biggs, N. L. and Ito, T. "Graphs with Even Girth and Small Excess." Math. Proc. Cambridge Philos. Soc. 88, 1-10, 1980.Wong, P. K. "Cages--A Survey." J. Graph Th. 6, 1-22, 1982.

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Excess

Cite this as:

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

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