Topology of whole-brain functional MRI networks: Improving the truncated scale-free model

Networks of connections within the human brain have been the subject of intense recent research, yet their topology is still only partially understood. We analyze weighted networks calculated from functional magnetic resonance imaging (fMRI) data acquired during task performance. Expanding previous work in the area, our analysis retains all of the connections between all of the voxels in the full brain fMRI data, computing correlations between approximately 200,000 voxels per subject for 10 subjects. We evaluate the extent to which this rich dataset can be described by existing models of scale-free or exponentially truncated scale-free topology, comparing results across a large number of more complex topological models as well. Our results suggest that the novel “log quadratic” model presented in this paper offers a significantly better fit to networks of functional connections at the voxel level in the human brain.