We perform targeted attack, a systematic computational unlinking of the network, to analyze its effects on global communication across the brain network through its giant cluster. Across diffusion magnetic resonance images from individuals in the UK Biobank, Adolescent Brain Cognitive Development Study and Developing Human Connectome Project, we find that targeted attack procedures on increasing white matter tract lengths and densities are remarkably invariant to aging and disease. Time-reversing the attack computation suggests a mechanism for how brains develop, for which we derive an analytical equation using percolation theory. Based on a close match between theory and experiment, our results demonstrate that tracts are limited to emanate from regions already in the giant cluster and tracts that appear earliest in neurodevelopment are those that become the longest and densest.
Keywords: connectomics; dMRI; network neuroscience; percolation theory; statistical mechanics.