Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits
Fig 2
Emergent higher-order connectivity features.
(A) Triad motif counts. Within each trial, the motif counts are averaged from 1000 randomly sampled quadruplets using the brain connectivity toolbox [28] and 100 control networks are generated to normalize the motif counts. The error bars show one SEM from 10 trials. The mean clustering coefficient is shown above each motif, with the non-zero ones highlighted in red. The asterisks denote the relative motif counts that are statistically significantly different from one (red asterisks p < 0.001, black asterisks p < 0.034; Holm step-down adjusted p-values [29]). (B) Left y-axis (blue): normalized rich-club coefficients Φ(k), which measures the extent to which the neurons with total degrees > k in a network are over-connected to each other. Within each trial, 100 control networks are generated to normalize the coefficients. The coefficient peaks at 1.60, which is significantly higher than 1 as given by the control networks (p < 0.001, one-sample t-test). Right y-axis (red): dynamical importance (averaged across neurons with the same total degree k within each trial), defined as the fractional change (%) in the largest eigenvalue of the adjacency matrix of the network upon removal of the neuron from it. The solid lines show the averages over 10 trials and the shaded areas show one SEM. Data for k < 200 is omitted from the plot because neurons with total degree k < 200 are sparse. (C) The rich-club curves with different common neighbor coefficients aΓ. Inset: the maximum rich-club coefficient between k = 500 and k = 600 are positively correlated with the common neighbor coefficient. Both motif and rich-club results are calculated for a circular region in the network containing 2000 excitatory neurons to avoid artefacts from the periodic boundaries.