Defining the urban "local" with low dimensional manifolds of human mobility networks

TL;DR

This paper introduces a topological framework that identifies localities within human mobility networks, revealing their geometric nature and low-dimensional manifold structure, which enhances urban modeling and spatial analysis.

Contribution

The study presents a novel topological approach to define and detect urban localities in mobility networks, linking them to geographic localities and demonstrating their low-dimensional manifold structure.

Findings

Human mobility network localities are geometric entities matching geographic localities.

Mobility networks lie on manifolds of dimension <=5.

The framework enables efficient spatial embedding and urban applications.

Abstract

Urban science has largely relied on universal models, rendering the heterogeneous and locally specific nature of cities effectively invisible. Here we introduce a topological framework that defines and detects localities in human mobility networks. We empirically demonstrate that these human mobility network localities are rigorous geometric entities that map directly to geographic localities, revealing that human mobility networks lie on manifolds of dimension <=5. This representation provides a compact theoretical foundation for spatial embedding and enables efficient applications to facility location and propagation modeling. Our approach reconciles local heterogeneity with universal representation, offering a new pathway toward a more comprehensive urban science.