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Table 1 Rounded centrality scores for the toy network: degree centrality (DC), betweenness centrality (BC), PageRank without teleportation (PR), and map equation centrality (\(\uplambda\)) for the one-level partition \({\mathsf {M}}_1\), a sub-optimal partition \({\mathsf {M}}_\text {sub}\), and the optimal partition \({\mathsf {M}}_\text {opt}\), shown in (Fig. 3)

From: Map equation centrality: community-aware centrality based on the map equation

u

DC

BC

PR

\(\uplambda ({\mathsf {M}}_1)\)

\(\uplambda ({\mathsf {M}}_\text {sub})\)

\(\uplambda ({\mathsf {M}}_\text {opt})\)

1

0.43

0.02

0.15

0.20

0.16

0.184

2

0.29

0

0.10

0.14

0.12

0.130

3

0.29

0

0.10

0.14

0.12

0.130

4

0.57

0.60

0.20

0.26

0.24

0.228

5

0.57

0.67

0.20

0.26

0.24

0.212

6

0.29

0

0.10

0.14

0.13

0.127

7

0.29

0

0.10

0.14

0.13

0.127

8

0.14

0

0.05

0.07

0.07

0.068