  This paper represents a contribution to the study of the brain functional
connectivity from the perspective of complex networks theory. More
specifically, we apply graph theoretical analyses to provide evidence of the
modular structure of the mouse brain and to shed light on its hierarchical
organization. We propose a novel percolation analysis and we apply our approach
to the analysis of a resting-state functional MRI data set from 41 mice. This
approach reveals a robust hierarchical structure of modules persistent across
different subjects. Importantly, we test this approach against a statistical
benchmark (or null model) which constrains only the distributions of empirical
correlations. Our results unambiguously show that the hierarchical character of
the mouse brain modular structure is not trivially encoded into this
lower-order constraint. Finally, we investigate the modular structure of the
mouse brain by computing the Minimal Spanning Forest, a technique that
identifies subnetworks characterized by the strongest internal correlations.
This approach represents a faster alternative to other community detection
methods and provides a means to rank modules on the basis of the strength of
their internal edges.
