Correlation between perturbation centrality and other centrality measures.

Perturbation centrality was compared to other centrality measures calculated as described in Supplementary Methods of Text S1. Spearman correlations above r = 0.7 are marked with bold letters, correlations below r = 0.3 are marked with italics. Highest correlations were observed between perturbation centrality versus closeness centrality, community centrality [29] and weighted degree. This underlines the observations that besides geodesic distance (closeness centrality), modular position and degree also contribute to good perturbation properties. Note that measured correlations between perturbation and closeness centralities are much weaker than the correlations between the reciprocal of fill time and closeness centrality (mean is 0.895 in Table S1 compared to 0.67 here, p = 0.000487, Wilcoxon rank-sum test; correlations with closeness centrality failed the Shapiro normality test with p = 0.0019)aNetwork descriptions are given in Supplementary Methods and Table S7 of Text S1.bCommunity centrality was calculated using the LinkLand community detection method of the ModuLand family as described by Kovács et al. [29].cPageRank values were calculated using the algorithm of the igraph library [59].