Extended Data Fig. 3: Computationally removing the distance dependence of connection weights alters the modular structure of the cortex.
From: Hierarchical organization of cortical and thalamic connectivity
To test the degree to which the spatial proximity of regions affects modularity analysis, we used a power law to fit the distance component of our ipsilateral CC connectivity matrix29. Then, we repeated our modularity analysis on the ‘distance-subtracted’ matrix built from these residuals. a, Weighted connectivity matrix for 43 cortical areas showing the value of the residuals from a power law to fit the distance component. Rows are sources, columns are targets. Colours on the rows indicate distance-subtracted community structure with varying levels of resolution (γ = 0.5–1.5 on the y-axis, γ = 0.8 only on the top portion of the x-axis). Columns are coloured by their module affiliation in the distance-subtracted matrix above their module affiliation in the original matrix (Fig. 1e). The inset in the top left corner shows the modularity metric (Q) for each level of γ, along with the Q value for a shuffled network containing the same weights. The Q values for modularity in the distance-subtracted matrix were smaller than for the original cortical matrix (for example, 0.2754 versus 0.4638 at γ = 0.8) and the range of values for which Q was greater than Qshuffled was narrower (0.7 ≤ γ ≤ 1.7), but some modules were still present in the distance-subtracted cortical connectivity matrix. The difference between Q and Qshuffled was greatest for γ = 0.8. The first distance-subtracted module was comprised of the entire somatomotor module, most of the lateral module, and two regions from the prefrontal module. The second distance-subtracted module contained the visual, auditory, and medial modules, plus most of the prefrontal module and one region from the lateral module (temporal association area). Notably, these modules were like those reported by Rubinov et al.9. As γ increased past 1.0, regions began to split from the two large modules in small groups that generally did not reflect the original divisions, except for the auditory areas. b, Ipsilateral cortical network in 2D using a force-directed layout algorithm. Nodes are colour coded by module. Edge thickness shows residual values and edges between modules are coloured as a blend of the module colours. c, Cortical regions colour-coded by their distance-subtracted community affiliation at γ = 0.8 show spatial relationships.
