Table 1 Tests of power-law model for the street-network evolution of the city of Dundee. The symbols are as follows. Number of street segments for each time period (n), scaling exponent based on MLE (α) (± shows the standard error on α), the number of observations in the power law range, ntail (± shows the standard error of the ntai)l, lower bound of power law (xmin) at which the power law model no longer applies (± shows the standard error of xmin), power law fits and the corresponding p-values and each of the subsequent rows shows the log likelihood ratios (LR) for the alternative models (fits) and the associated p-values. Positive values for LR indicate that the power law model is favoured over the alternative models if the p-value < 0.1. However, if the p-value is large than 0.1, the sign is not a reliable indicator as to which model provides the better fit to the data

From: Entropy and order in urban street networks

Tests of power law behaviour in street data sets

Dundee evolution

1600

1776–77

1821

1846

1912

2007

n

70

209

376

1360

2184

9616

α

3.46 ± 0.39

2.79 ± 0.42

2.71 ± 0.43

3.33 ± 0.14

2.93 ± 0.27

3.27 ± 0.09

ntail

32 ± 11

93 ± 30

185 ± 71

440 ± 110

615 ± 358

961 ± 241

x min

101 ± 23

108 ± 37

103 ± 50

100 ± 15

164 ± 57

165 ± 26

Power law

p

0.99

0.00

0.40

0.32

0.21

0.34

Log normal

LR

0.000

−3.388

−8.461

−1.198

−4.181

−0.402

 

p

0.57

0.22

0.00

0.17

0.04

0.29

Exponential

LR

3.048

−5.044

−9.436

19.214

24.124

90.124

 

p

0.89

0.11

0.00

0.98

0.96

0.99

Stretched

LR

0.048

−5.080

−9.520

−1.279

−4.169

−0.359

exponential

p

0.63

0.11

0.00

0.17

0.04

0.36