Figure 1

Statistics of the domain interaction network. (a). In the cumulative distribution of the expectation value of domain interactions we observe a heavy tail. Focusing on lower ranges of the expectation value, we approximated a power-law (P(E) ~ E^-2.7). The dependence of an interactions expectation value from the product of the domains degree k _i k _j shows a weak correlation (inset) (⟨E⟩ ~ k _i $k_j^{-0.04}$, Pearson's r = 0.30, P < 10^-5, Spearman's rank ρ = -0. 17, P < 10^-5, inset). (b) For single domain based measures such as the degree k and the strength s, we observe power-law tailed cumulative frequency distributions as well. Both distributions follow a generalized Zipf's law (P(k) = 8.7 × (2.1 + k)^-1.9, P(s) = 298.0 × (14.6 + s)^-2.0). (c) Indicating a networks modularity, the dependence of the clustering coeffcient C decays as a power-law, C(k) ~ k^-0.55. Basically, we observe the same correlation for the weighted clustering coeffcient C^w(k) ~ k^-0.47, indicating that the weighted generalization of the clustering coeffcient does not change the initial correlations. (d) The unweighted average nearest neighbor degree slightly decays with increasing degree. This albeit weak dependency is roughly approximated by a power-law (k _nn ~ k^-0.16). In principle, we obtain the same result for the weighted representation as well ($k_{nn}^w$ ~ k^-0.11). In (c) and (d), we logarithmically binned the data points and calculated mean values and standard deviations in each bin.