  The parametric geometry of numbers has allowed to visualize the simultaneous
approximation properties of a collection of real numbers through the combined
graph of the related successive minima functions. Several inequalities among
classical exponents of simultaneous approximation can be guessed by a study of
these graphs; in particular the so called regular graph is of major importance
as it provides an extremal case for some of these inequalities. The aim of this
paper is to define and construct an analogue of the regular graph in the case
of weighted simultaneous approximation.
