  This paper is motivated by the comparison of genetic networks based on
microarray samples. The aim is to test whether the differences observed between
two inferred Gaussian graphical models come from real differences or arise from
estimation uncertainties. Adopting a neighborhood approach, we consider a
two-sample linear regression model with random design and propose a procedure
to test whether these two regressions are the same. Relying on multiple testing
and variable selection strategies, we develop a testing procedure that applies
to high-dimensional settings where the number of covariates $p$ is larger than
the number of observations $n_1$ and $n_2$ of the two samples. Both type I and
type II errors are explicitely controlled from a non-asymptotic perspective and
the test is proved to be minimax adaptive to the sparsity. The performances of
the test are evaluated on simulated data. Moreover, we illustrate how this
procedure can be used to compare genetic networks on Hess \emph{et al} breast
cancer microarray dataset.
