A new flow-based centrality method for identifying statistically significant centers

Quantifying the centrality of places and identifying centers constitute the basis for assessing the urban spatial structure, which is essential for sustainable spatial planning. Both the existence and intensity of linkages contribute to the centrality of places. However, few centrality measures consider both aspects simultaneously. Additionally, the identification of centers often relies on specified minimum thresholds, which is subjective and arbitrary. To overcome these limitations, we propose a new flow-based centrality measure (MX-degree) inspired by the scientist's H-index, which effectively integrates flow volume and flow diversity automatically. Furthermore, we design a novel permutation strategy to test the significance of the MX-degree to identify the statistically significant centers. To demonstrate the validity of our method, we conduct a case study quantifying city centrality in China's two urban agglomerations: Beijing-Tianjin-Hebei (BTH) and Yangtze River Delta (YRD), based on population flow data. Specifically, the MX-degree outperforms other common centrality measures in reflecting cities' socioeconomic development levels. Significance tests show that the BTH region is dominated by the only statistically significant central city - Beijing, while the YRD region is more polycentric but with an uneven spatial distribution of central cities. Several implications for regional planning by the comparison of spatial structures are provided.