Statistics of domain strength. (a). The strength of a domain is defined as the sum of all expectation values of interactions a domain is involved in. The dependence of the strength from the domains degree shows a clear power-law s(k) ~ k1.04 (Pearson's r = 0.94, P < 10-5; Spearman's ρ = 0.93, P < 10-5), suggesting that connectivity and weights are widely independent. (b) The disparity value offers further support for this conclusion, since we find that Y2(k) ~ k-0.9 (Pearson's r = 0.43, P < 10-5; Spearman's ρ = 0.88, P < 10-5).