The weighting scheme in PR algorithms was using the weight of target and comparing it to the other destination originated from the source, to decide the probability of a random surfer moving from the source to the target PR could be understand as a special case of WPR that all node has the same weight. This scheme is also similar to the concept of radiation model, which is an alternative of the gravity model to understand human movement.
Radiation model is a parameter free spatial model, which suggested that the flow from a source to a target area depends only on the population of the two areas, and the population of the other areas whose distance from the source is less than the distance from the source to the target area [ 53 ]. The radiation model compares the target population to the population of other potential destination originated from the source and the interaction between the population of the potential destinations, to measure the strength of the links from the source to the target, which were than used to calculate the probability of a particle moving agent to be absorbed by the target from the source [ 54 ].
By using similar weighting scheme, WPR used the attractiveness of the target and compared it to the other potential destination. This means if there exist another destination whose attractiveness is same as the target, they would share the same probability, even if the second destination is farther away than the target from the source. Thus, the integration with the distance-decay function is necessary to capture the proximity differences between the destinations. Hence, GPR, which considered both attractiveness and distance-decay effects, could be an alternative to radiation model in a geospatial network analysis.
Moreover, regarding the modeling of spatial interactions among areas, moving agents could followed certain rules to be absorbed by any destination in radiation model; random surfers could only move within the network through the links in PR-family algorithms, and the probability of moving on each links depends only on the outgoing links of the source. The outgoing links are the only options for surfer moving from current location. The PR-family algorithms could reflect more realistic movement trajectories. On the other hand, global-wide urban road network data is openly and readily available from internet database, such as OpenStreetMap project.
Our algorithm could be more applicable than past extend models when we incorporated the link-node structures of road network and railways as a geometric graph to represent urban connections. In our study, geographic distance is formulated as spatial constraints in terms of distance-decay weighting scheme for measuring population mobility in national and city scales. Our results showed that the extended PR algorithm with the distance-decay properties and attraction properties captured the spatial patterns of population distribution.
Long travel distance could still act as impedance on population movement causing the decrease of interactions between areas even in the era of information and communication technology. This study has several limitations. First, types of nodes and links have been neglected. Because nodes represent different locations, some nodes may be residential areas with dense populations, some may be business areas with high volumes of traffic, and some may be industrial areas with massive man-made facilities. Therefore, different types of nodes could function differently in the geospatial network.
Second, we simplified nodal attraction, using the numbers of connections to each node. Additional approaches to nodal attraction may improve the correlation results, but they would also increase the complexity of the analysis. Third, in addition to node characteristics and nodal attraction, we also simplified connection types and capacities with bidirectional and unweighted links.
Although the algorithm was designed to explore the reachable relationships between spaces, the mode of movement and the number of paths could affect connectivity and the strength of links. Thus, the algorithm does not differentiate effects related to types and capacities of connections. These issues warrant further investigation. Geographic proximity and location attractiveness are important spatial factors in measuring the importance of locations.
At both the national scale and city scale, these proposed algorithms are more effective at capturing spatial patterns of human residence than other commonly-used network metrics. In comparing location attractiveness with distance-decay effects, we conclude that the spatial concentration of human movement is dominantly determined by distance-decay effects, which implies that geographic proximity remains a key influence on human mobility. The funder had no role in study design, data collection and analysis, or preparation of the manuscript. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
National Center for Biotechnology Information , U. PLoS One. Published online Oct 5. Author information Article notes Copyright and License information Disclaimer. Competing Interests: The authors have declared that no competing interests exist. Received May 13; Accepted Sep This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
This article has been cited by other articles in PMC. Abstract A network approach, which simplifies geographic settings as a form of nodes and links, emphasizes the connectivity and relationships of spatial features. Introduction Background The real world contains extensive connections. PageRank algorithm: Basic concepts and its extensions The PageRank algorithm can be regarded as a procedure for simulating the movement of random surfers within a web-page network connected by hyperlinks [ 16 ].
Open in a separate window. Fig 1. An illustration of PageRank algorithm. Geographic PageRank GPR : Incorporating effects of geographic proximity and attractiveness of locations Geographic considerations often consist of attractiveness and impedance among locations. Fig 2. Sensitivity of choosing distance-decay functions Distance-decay relationship is often formulated as power-law or exponential functions in geographical literatures [ 3 ]. Results Case Study 1: national-scale intercity network The national-scale case study area was the Taiwan Island, which has a population of approximately Fig 3.
Transformation from transportation system to geospatial network. Table 1 The correlation between the population density and the densities of total and incoming daily automobile flow for each township. Fig 4. Fig 5. Case Study 2: city-scale urban network Three major Taiwanese cities, with different geospatial characteristics, were used to analyze the usefulness of the city-scale urban network in identifying important locations with high concentrations of human movement.
Table 3 The summarized network statistics of the three cities. Area km 2 Junctions Settlements Number of links Network density d min km d max km Taipei 60 0. Fig 6.
Transportation and Economic Development | The Geography of Transport Systems
The robustness of methodological framework 1. Number of nodes in the K-means clustering procedure The settlements were used as the nodes in a geospatial network and were identified through the K-means clustering procedure. Fig 7. The rank correlation rho between different number of nodes k-value in range from to 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.
Distance factor in the power-law function Fig 9a and the left panel of Fig 10 a , 10 c and 10 e show the rank correlation of using different the values of distance factor in the power-law function for the national-scale and city-scale networks respectively. Fig 9.
Multiple Equilibria in the Urban Spatial Structure: Evidence from the Hanshin Earthquake
Fig Distance-decay functions: power-law vs. 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. Discussion With only relied on simplified transportation network streets and railways as a geometric graph to represent urban connections, our study captured the spatial distribution of population and mobility flows.
Conclusion Geographic proximity and location attractiveness are important spatial factors in measuring the importance of locations. References 1. Commoner M. Tobler W.
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