Figure 4

The association between the regionalization index and the community-level. (A) PageRank entropy, (B) betweenness centrality entropy, (C) flow hierarchy, (D) reciprocity, and (E) number of hierarchical layers. The regionalization index was positively associated with the community-level entropy of PageRank (\(R^{2} = 0.85\); \(p < 0.001\)) and betweenness centrality (\(R^{2} = 0.76\); \(p < 0.001\)); however, regionalization was negatively associated with flow hierarchy (\(R^{2} = 0.10\); \(p < 0.014\)), not linearly correlated with reciprocity (\(R^{2} = 0.05\); \(p = 0.07\)), and only weakly associated with the number of hierarchical layers (the mean regionalization index was significantly lower in communities with only a single hierarchical layer; ANOVA: \(\mbox{degrees of freedom} = 5\); \(\mbox{F value} = 7.245\); \(p < 0.001\); Tukey HSD test, with a correction for multiple comparisons, was used post-doc to determine which group means were different)