Intercity mobility reveals the hyperbolic geometry of city systems

TL;DR

This paper introduces a hyperbolic geometric model of intercity mobility that uncovers the hierarchical and proximity-based structures of city systems, validated across multiple datasets.

Contribution

A novel hyperbolic geometry framework for modeling city systems that captures the interplay of hierarchy and proximity in intercity mobility.

Findings

City hierarchies emerge bottom-up from mobility patterns.

Non-stationary variations in city-hinterland relations are driven by trade-offs.

Urban processes are shaped by trade-offs between hierarchy and hinterland range.

Abstract

The hierarchy and proximity are key dimensions of urban relational processes, but their interplay in shaping intercity interactions and the underlying structures of city systems remain unclear. We develop a novel geometric model of city systems embedding intercity mobility into a latent hyperbolic geometry, which unravels the measures of hierarchy and proximity accounting for their interplay. It is successfully validated against 12 different nationwide intercity mobility datasets. We find a bottom-up emergence of city hierarchies, along which the variations of city-hinterland relations are non-stationary in terms of their nesting and range properties. Such non-stationarity originates from trade-offs between city hierarchy and hinterland range in determining the formation of city-hinterland structures. Hierarchy- and proximity-dominated urban processes can be elucidated from examining dynamics of the trade-offs. The revealed urban relational processes of city systems are at the core of the emerging science of cities and crucial for spatial planning and regional policymaking.