Fig 1.
An illustration of PageRank algorithm.
The probabilities of a random surfer browsing from each web-page to the outgoing web-pages are assumed to be equal.
Fig 2.
The framework of DDPR and GPR algorithms.
Fig 3.
Transformation from transportation system to geospatial network.
Spatial distribution of (A) national-scale population centers and urbanization status, (B) junctions of the streets, and (C) the centroid nodes where people gathering together. Data souce: Institute of Transportation, MOTC (Taiwan).
Table 1.
The correlation between the population density and the densities of total and incoming daily automobile flow for each township.
Fig 4.
Spatial distributions of the: (A) DDPR and (B) GPR, and (C) urbanization status.
Table 2.
The spearman rank’s correlation between the PR algorithms, degree centrality and the concentration of human movement.
Fig 5.
Association between DDPR (a-c) and GPR (d-f) ranks with human movement concentration ranks.
(a) DDPR: population density; (b) DDPR: in-flow density; (c) DDPR: total flow density; (d) GPR: population density; (e) GPR: in-flow density; (f) GPR: total flow density. Most urban areas are clustered in the upper-right area of each plot in the figure, indicating that they are rated as having high DDPR and GPR rankings and as areas with high-concentration of human movement. On the other hand, most rural area nodes are clustered in the bottom-left areas of the plots, indicating that such areas are rated as having low DDPR and GPR rankings and as areas with low-concentration of human movement. Most nodes in the upper-left area of the plot are urbanized areas, which suggests that the ranks of high-level urbanized areas could be underrated by the DDPR and GPR scores.
Table 3.
The summarized network statistics of the three cities.
Fig 6.
The spatial distribution of nodes with underlying network; the DDPR and GPR ranks results.
The spatial distribution of nodes with underlying network for: (a) Taipei city; (b) Taichung city; (c) Kaohsiung city. DDPR ranks result with 0.5 hour transportation network for: (d) Taipei city; (e) Taichung city; (f) Kaohsiung city; and GPR ranks result for: (g) Taipei city; (h) Taichung city; (i) Kaohsiung city. The size of the nodal circle is proportional to the ranks of DDPR or GPR scores. The nodes with higher rankings are concentrated in the central area in Taipei City (d,g), in the southern inner area in Taichung City (e,h), and in the southern coastal area in Kaohsiung City (f,i). These higher-ranking nodes capture the locations of central business district (CBD) among the three cities. The lower ranking nodes are located in the outer rings of Taipei City. The northern Taichung, with lower rankings, is separated from the CBD by a river. In Kaohsiung City, the areas with lower rankings are concentrated in the northern underdeveloped regions. Data souce: Institute of Transportation, MOTC (Taiwan).
Table 4.
The Spearman’s rank correlation (rho) between the network metrics and the population density for the three cities.
Fig 7.
The rank correlation (rho) between different number of nodes (k-value) in range from 100 to 750 and the population density in national scale.
Fig 8.
The rank correlation (rho) between different number of nodes (k-value) in range from 20 to 85 and the population density in city scale.
(a) Taipei City; (b) Taichung City; (c) Kaohsiung City.
Fig 9.
The rank correlation (rho) between the population density and the different (a) β and (b) γ values in national scale.
Fig 10.
The rank correlation (rho) between the population density and the different values of β (left) and γ (right) in the three cities.
Table 5.
The optimal parameter settings and correlation results of DDPR with power-law and exponential decay functions.
Table 6.
The optimal parameter settings and correlation results of GPR with power-law and exponential decay functions.