X-index: A novel flow-based locational measure for quantifying centrality

The centrality of a place reflects its relative importance in serving other places, and quantifying centrality is a prerequisite for assessing the urban spatial structure and facilitates policy-making of sustainable urban development. Two important aspects in quantifying the centrality of a place are the amount of service it provides to other places and the spatial diversity of the places it serves. For example, a central city attracts not only many people but also people from various cities. However, few existing centrality measures can address the two aspects simultaneously. In this study, following the idea of the scholar’s H-index, we propose a novel flow-based locational measure, the X-index, which quantifies the centrality of a place by considering both the volume and directions of flows toward the place in an automated way. We demonstrate the effectiveness and advantages of the X-index over other common centrality measures by quantifying the centrality of Chinese cities and spatial grid cells in Beijing. The results show that: (1) The X-index can successfully detect all the official national central cities and reveal the hierarchy of cities. (2) The X-index is positively correlated with the variety of urban functions in grid cells, which is consistent with central place theory.