Fig. 4

Effect of excitation-inhibition (1) balance in network topology. Panel (a): probability distribution function of the structural connectivity weights in controls and patients before (unnormalized) and after (normalized) homeostatic plasticity (see main text, Eq. (1)). For each group, the non-zero weights of all individual matrices were pooled together and then the histogram was computed leading to a representative PDF for the corresponding group. The black lines are power law fits (\(p \sim W_{ij}^{-\alpha }\)) in the region of the log-log graph with linear behavior, with exponents obeying \(\alpha _{nor} =2,15\) and \(\alpha _{un}=4,25\), for the normalized and unnormalized distributions, respectively. Note enhancement of network heterogeneity following homeostatic plasticity. Panel (b): connectivity disorder (i.e., structural entropy, Eq. (12)) for all patients and controls for normalized and unnormalized connectivity matrices. Controls are colored in blue (\(n=46\)). Brown dots represent patients at \(t_1\) (3 months post-stroke, \(n=54\)), while green dots at \(t_2\) (12 months post-stroke, \(n=59\)). Normalized density plots (histograms) are also shown. Inclusion of excitation-inhibition balance drastically increases both, the connectivity disorder (i.e., entropy) and the separation of the PDFs between controls and stroke patients and between stroke patients at different time-points.