Quantifying urban areas is crucial for addressing associated urban issues such as environmental and sustainable problems. Remote sensing data, especially the nighttime light images, have been widely used to delineate urbanized areas across the world. Meanwhile, some emerging urban data, such as volunteered geographical information (e.g., OpenStreetMap) and social sensing data (e.g., mobile phone, social media), have also shown great potential in revealing urban boundaries and dynamics. However, consistent and robust methods to quantify urban areas from these multi-source data have remained elusive. Here, we propose a percolation-based method to extract urban areas from these multi-source urban data. We derive the optimal urban/non-urban threshold by considering the critical nature of urban systems with the support of the percolation theory. Furthermore, we apply the method with three open-source datasets -population, road, and nighttime light -to 28 countries. We show that the proposed method captures the similar urban characteristics in terms of urban areas from multi-source data, and Zipf's law holds well in most countries. The derived urban areas by different datasets show good agreement with the Global Human Settlement Layer (GHSL) and can be further improved by data fusion. Our study not only provides an efficient method to quantify urban areas with open-source data, but also deepens the understanding of urban systems and sheds some light on the multi-source data fusion in geographical fields.lacking in many developing countries. Second, the data collection process for MAs is time-consuming and expensive, making it unable to capture the rapid urbanization process in fast-growing regions. Third, the standard to define MAs is different in different countries. There is still a lack of a unified approach to obtain functional urban areas, which can be applicable to all countries.
Betweenness centrality (BC) is widely used to identify critical nodes in a network by exploring the ability of all nodes to act as intermediaries for information exchange. However, one of its assumptions, i.e., the contributions of all shortest paths are equal, is inconsistent with variations in spatial interactions along these paths and has been questioned when applied to spatial networks. Hence, this paper proposes a spatial interaction incorporated betweenness centrality (SIBC) for spatial networks. SIBC weights the shortest path between each node pair according to the intensity of spatial interaction between them, emphasizing the combination of a network structure and spatial interactions. To test the rationality and validity of SIBC in identifying critical nodes and edges, two specific forms of SIBC are applied to the Shenzhen street network and China’s intercity network. The results demonstrate that SIBC is more significant than BC when we also focus on the network functionality rather than only on the network structure. Moreover, the good performance of SIBC in robustness analysis illustrates its application value in improving network efficiency. This study highlights the meaning of introducing spatial configuration into empirical models of complex networks.
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