We performed two distinct operations to alter the long-range connectivity: thresholding, which is based on the number of tracks between vertices (weight-based), and trimming, which is based on the average track length between vertices (distance-based).

Long-range connectivity thresholding.For thresholding, the z-scored weighted long range connectivity matrix C^z (Eq. 4) was binarized according to an adjacency weight threshold value zC. The ratio r of local versus long-range connections is defined as r=tr(Aℓ)/(tr(Aℓ)+tr(Ac)), which is the number of local connections divided by the summed numbers of local and long-range connections. Because the local gray matter connectivity matrix is determined by the cortical surface mesh and the diffusion kernel, we kept it constant (unless otherwise mentioned) and varied the white matter connectivity threshold zC, which thereby controls the proportion r of local connections. As weights represent the number of streamlines connecting distant nodes, when zC increases, only the most prominent tracks of the white matter remain.

Long-range connectivity trimming.Trimming was simulated by removing some percentage η of the long range connectivity entries based on their average track length. Different scenarios were implemented: 1) removing the longest tracks first; 2) removing the shortest tracks first; and 3) removing tracks in random order. Note that we applied trimming to the long-range white matter connections after applying the threshold zC=1, thereby setting the proportion of local connections to r ≃ 0.7. Thus, the reported percentage of trimming affected only the remaining long-range white matter connections after thresholding.

Callosectomy.Finally, we introduce the removal of inter-hemispheric connections in a process termed callosectomy, whereby inter-hemispheric connections are removed either randomly (with probability κ) or by descending order of track lengths. A visualization of the resulting graphs structure for gradual values of κ is provided in Suppl. Figure 10 for illustrative purpose.