Graph coarse-graining reveals differences in the module-level structure of functional brain networks

Abstract: 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.