Figure 7
Closeness and Betweeness centralities. Closeness centrality. V 1 : d1 = 4 × 1 + 1 × 2 + 1 × 3 = 9, C clo (1) = 6/9. V 1 accesses 4 nodes (V 2 , V 5 , V 6 , V 7 ) with step 1, 1 node (V 3 ) with step 2 and 1 node (V 4 ) with step 3. 6 nodes can be accessed in total by V1. V 2 : d2 = 2 × 1 + 4 × 2 = 10 > d1, C clo (2) = 6/10. V 2 accesses 2 nodes (V 1 , V 3 ) with step 1 and 4 nodes (V 4 , V 5 , V 6 , V 7 ) with step 2. 6 nodes can also be accessed in total by V2. As a result, V1 is more central than node V2 since d1>d2. Betweenness centrality. N p (1) = 12 shortest paths that pass through node V 1 . The paths from the starting to the ending node are {V 2 -V 5 , V 2 -V 6 , V 2 -V 7 , V 3 -V 5 , V 3 -V 6 , V 3 -V 7 , V 4 -V 5 , V 4 -V 6 , V 4 -V 7 , V 5 -V 6 , V 5 -V 7 , V 6 -V 7 }. N p (2) = 8 shortest paths that pass through node V 2 . The paths are {V 1 -V 3 , V 1 -V 4 , V 3 -V 5 , V 3 -V 6 , V 3 -V 7 , V 4 -V 5 , V 4 -V 6 , V 4 -V 7 }. N p (3) = 5 {V 1 -V 4 , V 2 -V 4 , V 4 -V 5 , V 4 -V 6 , V 4 -V 7 }. N p (4) = N p (5) = N p (6) = N p (7) = 0. N p = 25 the total sum of shortest paths that pass through the nodes, thus N p = N p (1)+N p (2)+N p (3)+N p (4)+N p (5)+N p (6)+N p (7). The centralities are C b (1) = 12/25 = 0.48, C b (2) = 8/25 = 0.32, C b (3) = 5/25 = 0.20, C b (4) = C b (5) = C b (6) = C b (7) = 0, thus node V 1 is more central.