  Network analysis is rapidly becoming a standard tool for studying functional
magnetic resonance imaging (fMRI) data. In this framework, different brain
areas are mapped to the nodes of a network, whose links depict functional
dependencies between the areas. The sizes of the areas that the nodes portray
vary between studies. Recently, it has been recommended that the original
volume elements, voxels, of the imaging experiment should be used as the
network nodes to avoid artefacts and biases. However, this results in a large
numbers of nodes and links, and the sheer amount of detail may obscure
important network features that are manifested on larger scales. One fruitful
approach to detecting such features is to partition networks into modules, i.e.
groups of nodes that are densely connected internally but have few connections
between them. However, attempting to understand how functional networks differ
by simply comparing their individual modular structures can be a daunting task,
and results may be hard to interpret. We show that instead of comparing
different partitions, it is beneficial to analyze differences in the
connectivity between and within the very same modules in networks obtained
under different conditions. We develop a network coarse-graining methodology
that provides easily interpretable results and allows assessing the statistical
significance of observed differences. The feasibility of the method is
demonstrated by analyzing fMRI data recorded from 13 healthy subjects during
rest and movie viewing. While independent partitioning of the networks
corresponding to the the two conditions yields few insights on their
differences, network coarse-graining allows us to pinpoint e.g. the increased
number of intra-module links within the visual cortex during movie viewing.
