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Table 1 Catchment areas with different center (blue) nodes and indicator values of (red) node under investigation in the selected catchment areas

From: Normalized closeness centrality of urban networks: impact of the location of the catchment area and evaluation based on an idealized network

  

Distance between red chosen node and blue center node

m

Closeness centrality of the red chosen node

Average distance from all nodes to chosen node

Total number of nodes

Normalized closeness centrality

 

C(v)

\(\sum_{n=1}^{N}S\left(v,n\right)/(N-1)\)

N

CN(v)

Unit

1/km

m

1/km

Catchment area 1

0

0.000678

917

1606

1.089

Catchment area 2

50

0.000674

906

1637

1.103

Catchment area 3

100

0.000668

899

1665

1.112

Catchment area 4

200

0.000649

891

1728

1.12

Catchment area 5

300

0.000635

874

1802

1.145

Catchment area 6

500

0.000611

854

1916

1.170

Catchment area 7

1000

0.000528

918

2062

1.088

Catchment area 8

1500

0.000438

1190

1919

0.840

  1. aThe length of any link between two nodes can be calculated with a simple Pythagoras’ Theorem