Fig 1.
Street networks of metropolitan area delimited by orbital roads— M25 for London and 6th ring for Beijing.
Left panel: London street network (source: UK Ordance Survey (see S1 Appendix), Using: Meridian 2 Digimap Ordnance Survey Service). London street network is governed by dendritic pattern. Right panel: Beijing street network (source: Open Street Map (OSM) (see S1 Appendix), Using: Road Shapefile Layer). Beijing street network is dominated by grid-like pattern.
Fig 2.
Histogram of degree distribution in the primal space for London (Left) and Beijing (Right).
Fig 3.
Betweenness centrality on the street networks, which is calculated from the dual space.
Left panel: London; Right panel: Beijing. The roads with maximum betweenness centrality in London and Beijing are orbital roads (M25 for London and 4th ring for Beijing). Map composed in ESRI ArcGIS 10.1.
Fig 4.
Closeness gradient maps in the primal space.
Left panel: London; Right panel: Beijing. Dark dots are places with higher closeness centrality. The colours are decayed from centre to periphery in the both cities. Map composed in ESRI ArcGIS 10.1.
Fig 5.
Left panel: Degree density and cumulative distribution in dual space for London. Right panel: Degree density and cumulative distribution in dual space for Beijing.
Fig 6.
Upper panels: road length of street network as a function of connectivity degree in the dual space for London (Left) and Beijing (Right). Dark point is road length associated with the vertex degree. Red point is value representative of binned data with error bar. Bottom panels: betweenness centrality as a function of connectivity degree in dual space for London (Left) and Beijing (Right). Dark point is betweenness centrality associated with the vertex degree. Red point is value representative of binned data with error bar.
Table 1.
Summary of topological and geometrical properties in London and Beijing.
Fig 7.
Maximum cluster size and second largest cluster size as a function of proportion of edges removed in the primal space under the random attack scenario.
Gray dot is maximum cluster size; Blue dot is maximum cluster size averaged over one hundred realisations with error bar; Dark dot is second largest cluster size; Red dot is second largest cluster size averaged over one hundred realisations with error bar. Upper left panel: ERPG; Upper right panel: GRID; Bottom left panel: London; Bottom right panel: Beijing.
Fig 8.
Maximum cluster size and second largest cluster size as a function of proportion of edges removed in the primal space under the intentional attack scenario.
Gray dot is maximum cluster size; Blue dot is maximum cluster size averaged over one hundred realisations with error bar; Dark dot is second largest cluster size; Red dot is second largest cluster size averaged over one hundred realisations with error bar. Upper left panel: ERPG; Upper right panel: GRID; Bottom left panel: London; Bottom right panel: Beijing.
Fig 9.
Maximum cluster size and second largest cluster size as a function of proportion of edges removed in the dual space under the random attack scenario.
Gray dot is maximum cluster size; Blue dot is averaged maximum cluster size over one hundred realisations with error bar; Dark dot is second largest cluster size; Red dot is averaged second largest cluster size over one hundred realisations with error bar. Upper left panel: ERPG; Upper right panel: GRID; Bottom left panel: London; Bottom right panel: Beijing.
Fig 10.
Maximum cluster size and second largest cluster size as a function of proportion of edges removed in the dual space under the intentional attack scenario.
Gray dot is maximum cluster size; Blue dot is maximum cluster size averaged over one hundred realisations with error bar; Dark dot is second largest cluster size; Red dot is second largest cluster size averaged over one hundred realisations with error bar. Upper left panel: ERPG; Upper right panel: GRID; Bottom left panel: London; Bottom right panel: Beijing.
Fig 11.
Length distribution in dual space for London and Beijing.
Long-range connections across the networks such as M25 in London and 3th–6th rings in Beijing are highlighted by the red circles.
Fig 12.
Boxplot of critical points over one hundred realisations under the random and intentional attack scenarios in the primal and dual space for each net.
Left panel: primal space. Right panel: dual space. Dashed red lines within the boxes are the critical points calculated by second largest cluster size averaged over one hundred realisations shown in Table A in S1 Appendix.
Fig 13.
Network efficiency as a function of proportion of edges removed on the street networks under the random (left panel) and intentional (right panel) attack scenarios. Gray dot is network efficiency; Colour dot is network efficiency averaged over one hundred realisations with error bar, where Red is ERPG, Blue is GRID, Pink is Beijing, and Green is London.