Graph complexity and the laplacian matrix in blocked experiments

Abstract

connections between the efficiency of statistical designs, the Laplacian matrix studied in algebra, and graphs of maximal complexity are being described. Up to a positive scalar multiple the Laplacian (or Kirchhoff) matrix concides with the information matrix that arises out of a statistical additive model with treatment and block effects. By way of the matrix-tree theorem design efficiency is shown to be closely related to graph complexity. Several open questions regarding graphs of maximal complexity are being brought to attention.

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