The topological organization of human brain networks can be mathematically characterized by the connectivity degree distribution of network nodes. However, there is no clear consensus on whether the topological structure of brain networks follows a power law or other probability distributions, and whether it is altered in Alzheimer’s disease (AD). Here we employed resting-state functional MRI and graph theory approaches to investigate the fitting of degree distributions of the whole-brain functional networks and seven subnetworks in healthy subjects and individuals with amnestic mild cognitive impairment (aMCI), i.e., the prodromal stage of AD, and whether they are altered and correlated with cognitive performance in patients. Forty-one elderly cognitively healthy controls and 30 aMCI subjects were included. We constructed functional connectivity matrices among brain voxels and examined nodal degree distributions that were fitted by maximum likelihood estimation. In the whole-brain networks and all functional subnetworks, the connectivity degree distributions were fitted better by the Weibull distribution [f(x)~x(β−1)e(−λxβ)] than power law or power law with exponential cutoff. Compared with the healthy control group, the aMCI group showed lower Weibull β parameters (shape factor) in both the whole-brain networks and all seven subnetworks (false-discovery rate-corrected, p < 0.05). These decreases of the Weibull β parameters in the whole-brain networks and all subnetworks except for ventral attention were associated with reduced cognitive performance in individuals with aMCI. Thus, we provided a short-tailed model to capture intrinsic connectivity structure of the human brain functional networks in health and disease.

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