A Century of Topological Coevolution of Complex Infrastructure Networks in an Alpine City
Table 2
Statistical tests of the small world (C: average clustering coefficient; : characteristic path length; and : ratio indicating the small-world property) and power-law hypotheses (: scaling parameter; : lower bound for curve fitting; p value: goodness-of-fit for power-law hypothesis) over time for the WDN, UDN, and RN according to Telesford et al. [31] and Clauset et al. [24].
Year
C
ω
p value
WDN
UDN
RN
WDN
UDN
RN
WDN
UDN
RN
WDN
UDN
RN
WDN
UDN
RN
1910
0.026
0.212
-
9.86
6.18
-
0.652
0.300
-
3.29 (2)
3.25 (3)
-
0.158
0.169
-
1920
0.030
0.194
-
11.09
8.95
-
0.579
0.146
-
3.28 (2)
3.40 (3)
-
0.565
0.365
-
1930
0.025
0.187
-
12.47
9.66
-
0.559
0.117
-
3.23 (2)
3.45 (3)
-
0.016
0.518
-
1940
0.025
0.192
0.172
16.16
9.32
8.58
0.436
0.133
0.164
3.27 (2)
3.50
2.78 (3)
0.015
0.754
0.021
1950
0.026
0.189
0.180
17.16
9.30
8.75
0.405
0.161
0.095
3.29 (2)
3.57 (3)
2.69
0.102
0.348
0.008
1960
0.034
0.176
0.175
14.79
11.58
8.54
0.442
0.080
0.117
3.28 (2)
3.76 (5)
2.68 (3)
0.084
0.111
0.038
1970
0.039
0.161
0.181
14.25
12.06
8.20
0.440
0.120
0.134
3.50 (3)
3.50
2.69(3)
0.187
0.003
0.005
1980
0.043
0.162
0.181
13.71
18.38
7.97
0.443
-0.088
0.140
3.47 (3)
3.50
2.67 (3)
0.238
0.004
0.010
1990
0.039
0.161
0.180
13.42
15.64
8.01
0.468
-0.020
0.142
3.45 (3)
3.50
2.67 (3)
0.791
0.002
0.047
2000
0.039
0.159
0.180
12.92
16.59
7.99
0.484
-0.041
0.147
3.39 (3)
3.50
2.68 (3)
0.257
0.001
0.110
2010
0.042
0.160
0.185
12.74
16.92
8.04
0.481
-0.063
0.123
3.37
3.50
2.72 (3)
0.051
0.002
0.694
recalculated to maximize p value from/to: = (5)/(3); (9)/(3); (4)/(3); p values ≥ 0.1 proving the power-law hypothesis are shown in bold (50% of the networks).
