My understanding of Craddock et al. (2012), page 1917, is that they consider two different similarity measures: r_t, which is the correlation between the time-series; r_s which is the correlation between the spatial maps (maps of voxel-wise time-series correlations like r_t, if I've understood correctly). Isn't the former just your D_mn, rather than transforming D to W to S?

On a somewhat related note, could your approach be applied for arbitrary similarity matrix (or negated distance matrix) in place of connectivity matrix D? E.g. could it be used as an alternative to hierarchical clustering (etc) for segmenting (connected subregions of) tissues from a single (or multi-modal set of) structural MRI of a subject?