Excess

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

In graph theory, excess refers to the quantity

(1)

for a -regular graph  on  nodes with girth , where

(2)

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

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.