Table 1. Correlation between perturbation centrality and other centrality measures.

Networksa	Closeness centrality	Betweenness centrality	Community centralityb	PageRankc	Degree	Weighted degree
Benchmark graphs with pronounced modules	0.79	0.31	0.30	0.08	0.26	0.26
Benchmark graphs with fuzzy modules	0.79	0.76	0.83	0.67	0.83	0.83
Substrate-free Met-tRNA synthetase protein structure network	0.86	0.44	0.26	0.16	0.38	0.34
Substrate-bound Met-tRNA synthetase protein structure network	0.87	0.44	0.25	0.18	0.41	0.37
Filtered Yeast Interactome	0.09	0.33	0.80	0.47	0.67	0.85
Database of Interacting Proteins yeast interactome (release 2005)	0.62	0.56	0.84	0.73	0.66	0.72
Database of Interacting Proteins yeast interactome (release 2010)	0.67	0.41	0.63	0.47	0.52	0.65
E. coli metabolic network	0.72	0.31	0.97	0.67	0.59	0.99
B. aphidicola metabolic network	0.70	0.40	0.98	0.78	0.72	0.99
School-friendship network	0.68	0.43	0.69	0.58	0.68	0.71
Mean and standard error	0.67 (0.063)	0.44 (0.043)	0.65 (0.090)	0.48 (0.081)	0.57 (0.056)	0.69 (0.087)

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].