  In this work, we look at a two-sample problem within the framework of
Gaussian graphical models. When the global hypothesis of equality of two
distributions is rejected, the interest is usually in localizing the source of
difference. Motivated by the idea that diseases can be seen as system
perturbations, and by the need to distinguish between the origin of
perturbation and components affected by the perturbation, we introduce the
concept of a minimal seed set, and its graphical counterpart a graphical seed
set. They intuitively consist of variables driving the difference between the
two conditions. We propose a simple testing procedure, linear in the number of
nodes, to estimate the graphical seed set from data, and study its finite
sample behavior with a stimulation study. We illustrate our approach in the
context of gene set analysis by means of a publicly available gene expression
dataset.
