Fig 1.
World map showing locations of downloaded city extracts for 2014 and 2019.
The geodata used to render the plot is from OpenStreetMap [27] by way of Mapzen’s MetroExtracts (2014, [28]) and Nextzen’s MetroExtracts (2019, [30]) The figure was rendered using Python’s geopandas package [31].
Fig 2.
Conurbations of Samara-Tolyatti (Russia) and Kansas City-Lawrence-Topeka (USA) showing their road networks.
The geodata used to render the plot is from OpenStreetMap [27] by way of Mapzen’s MetroExtracts [28]. The road networks were rendered using Python’s pyrosm package [32].
Fig 3.
Schematic of a road network before (left) and after (right) application of the reduction process.
Fig 4.
Dependence of , the time needed to reach a percentage q of nodes, on pd, the fraction of road segments damaged, for five sample city road networks.
The road segments damaged were chosen at random. Averages were computed for 100 randomly—chosen trial locations for a relief center.
Fig 5.
Gap statistic plots for standardized damage response variables (Zslope, Zintercept and ) of world cities in 2014 (a) and 2019 (b).
The number of clusters, k, chosen for each dataset is marked by a dashed line. Clusters were generated using complete—linkage hierarchical clustering. The generation of clusters, gap statistics and plots were generated using implementations within R’s factoextra package.
Table 1.
Principal component loadings and cumulative variance of the standardized damage response of city road networks: Slope (Zslope), intercept (Zintercept) and r2 ().
In both sets of city road networks, the damage response can effectively be reduced from three to two dimensions. The first component simultaneously encodes a road network’s susceptibility to damage; the second component, smaller in contribution than the first, encodes the unpredictability of the network’s damage response.
Table 2.
Mean and standard deviation for the computed network properties and damage response variables (slope, intercept and r2) for the road networks of 201 (2014) and 194 (2019) cities worldwide.
Data extracted from OpenStreetMap (OSM) through the Metro Extracts services of Mapzen (2014) and Nextzen (2019).
Fig 6.
Road networks of 201 (2014) and 194 (2019) cities around the world.
These are hierarchically clustered according to their standardized damage response variables: slope (Zslope), y—intercept (Zintercept) and r2 (). The number of clusters chosen for each set of road networks (5 for 2014, 4 for 2019) was selected taking parsimony and fine structure considerations into account, as discussed in the Methodology.
Fig 7.
Frequencies for examined cities according to population density (2014 and 2019 datasets), 2014 GDP per capita (2014 dataset) and per-capita GDP growth from 2014 to 2016 (2019 dataset).
For each road network dataset, the clusters obtained are colored as in their respective dendrograms in Fig 6.
Fig 8.
Principal-component projections of standardized damage response variables for the road networks of 201 (2014) and 194 (2019) cities worldwide: Slope (Zslope), intercept (Zintercept) and r2 ().
For each road network dataset, the clusters obtained are colored as in their respective dendrograms in Fig 6.
Fig 9.
Damage response of five sample cities, together with their respective road networks.
Each city and road network was selected from one 2014 cluster each.
Table 3.
Regression coefficients of generalized linear models for the principal components PC1 and PC2 for 2014 and 2019 city road networks.
The standard error for each coefficient is in parentheses. Coefficients exhibiting statistical significance under a two-tailed t-test are marked with asterisks.