  Inferring brain connectivity network and quantifying the significance of
interactions between brain regions are of paramount importance in neuroscience.
Although there have recently emerged some tests for graph inference based on
independent samples, there is no readily available solution to test the change
of brain network for paired and correlated samples. In this article, we develop
a paired test of matrix graphs to infer brain connectivity network when the
groups of samples are correlated. The proposed test statistic is both bias
corrected and variance corrected, and achieves a small estimation error rate.
The subsequent multiple testing procedure built on this test statistic is
guaranteed to asymptotically control the false discovery rate at the
pre-specified level. Both the methodology and theory of the new test are
considerably different from the two independent samples framework, owing to the
strong correlations of measurements on the same subjects before and after the
stimulus activity. We illustrate the efficacy of our proposal through
simulations and an analysis of an Alzheimer's Disease Neuroimaing Initiative
dataset.
