Human Mobility Network Localities

• Human Mobility Network Localities are subnetworks defined by strong internal mobility flows, detected via a dichotomy-based topological framework.
• Empirical validation shows these localities align closely with geographic clusters and can be embedded in a low-dimensional manifold (dimension ≤5).
• The methodology enables practical applications such as optimizing facility locations and improving epidemic diffusion models through scalable, data-driven urban analysis.

Human mobility network localities are rigorously defined subnetworks or “open sets” within large-scale human mobility networks, corresponding to groups of places that are more strongly interconnected in terms of observed mobility flows than with locations outside their boundary. These localities exhibit both geometric and topological properties that map directly onto underlying geographic patterns. Advanced network analysis reveals that these localities reside on low-dimensional manifolds (with dimension ≤5), allowing for efficient representation, interpretation, and application in urban science, facility optimization, and epidemic modeling (Jiang et al., 20 Oct 2025).

1. Topological Framework for Defining Localities

The foundational contribution is a dichotomy-based topological framework for locality detection. Given a center node O in a human mobility network (for instance, an urban census tract or a transportation hub), its neighboring nodes are sorted by increasing distance derived from edge weights (where network “distance” is inversely related to the strength or frequency of mobility flow). This ordering reveals a bifurcation: a set B¹ of neighbors almost equidistant to O that continues the locality, and a set B² that is abruptly farther, establishing a natural locality boundary.

Formally, the network is equipped with a hyperbolic-like distance:

$x_{ij} = C + \ln(S_i S_j / w_{ij}),$

where $w_{ij}$ is the edge weight (mobility flow between nodes $i$ and $j$), $S_i$ is a node-specific scaling factor, and $C$ is a constant chosen to ensure the triangle inequality. The dichotomy of neighbors satisfies the local “open set” requirement for a manifold structure.

This differentiates the method from previous approaches relying on distance-decay, gravity, or opportunity models by constructing localities endogenously from the network’s weighted topology, not by imposing a parametric form on flows.

2. Empirical Validation and Geometric Correspondence

Empirical validation leverages dichotomy analysis and statistical comparison with spatial geography. When the nearest neighbors of a node O are divided into B¹ and B² according to the derived network distance, the B¹ nodes are statistically much closer in geographic space than the B² nodes. Quantitative t-tests across numerous samples demonstrate that the constructed network-based localities (via dichotomy) correspond tightly to geographic localities—that is, nodes grouped via mobility flows form clusters matching real spatial proximity.

Moreover, within these defined network localities, internal connectivity (measured by sum of edge weights or network conductance) is substantially higher than connectivity to external nodes, solidifying their interpretation as mobility-dense subgraphs.

3. Manifold Dimensionality and Compact Representation

A central result is that the detected localities and the full human mobility network can be embedded into a manifold of dimension no greater than five. This bound is substantiated by a percolation argument: by assessing the connectedness of size-6 localities in geographic space and using continuum percolation thresholds, intersection patterns restrict the effective dimension.

Consequently, the manifold representation compresses diverse, heterogeneous local mobility patterns into a compact geometric object, capturing both city-scale and neighborhood-scale structure. This enables multidimensional data reduction while preserving topological relationships vital for modeling and further analysis.

4. Applications: Facility Location and Propagation Modeling

Two major applications exemplify the impact of this framework:

• Facility Location Optimization: By embedding urban mobility networks onto the low-dimensional manifold and then population-equalizing via cartogram transformation, optimal placement of facilities (e.g., service centers, medical facilities) produces a uniformly spaced solution. This matches central place theory predictions for uniform spaces and demonstrates the utility of the manifold as a basis for equitable resource allocation.
• Epidemic and Diffusion Modeling: In propagation models (such as COVID-19 diffusion), embedding the network on the manifold removes geometric heterogeneities of the underlying geography. Simulated or real contagions on the manifold exhibit isotropic, concentric diffusion fronts, facilitating straightforward and accurate modeling of epidemic spread mechanisms that typically appear distorted in raw geographic coordinates.

5. Reconciling Local Heterogeneity with Universal Representation

The framework provides a systematic means to preserve local heterogeneity—arising from differences in urban form, socio-spatial practices, or infrastructure—while simultaneously permitting universal, low-dimensional representation. Every node’s locality is derived from its specific network context (heterogeneity), but through isometric manifold embedding (e.g., topologically consistent isometric embedding, TCIE), these diverse local forms are integrated into a globally consistent geometric space. This resolves the long-standing urban science challenge of integrating locality-specific dynamics into scalable, transferable models.

6. Future Research Directions and Broader Implications

Several future research avenues arise from these findings:

• Extension to dynamic and multi-layer networks, capturing temporal evolution and interaction among different mobility, socioeconomic, or infrastructural layers.
• Refinement of embedding algorithms and topological metrics (e.g., hyperbolic distance calibration, improved open set criteria) to better serve cities with highly non-uniform urban structures.
• Application beyond spatial analysis, such as integrating mobility, land use, and social network layers for holistic urban modeling.
• Development of policy tools—enabled by manifold embeddings—for simulating interventions (facility placement, infrastructure changes, targeted quarantines) in local or global urban contexts.

This framework thus marks a significant advancement in urban science and network-based mobility analysis by rigorously defining and detecting human mobility network localities as geometric objects embedded in low-dimensional space. It bridges the gap between local specificity and universal scalability, directly supporting applications in facility optimization, epidemic modeling, and multidomain urban analytics (Jiang et al., 20 Oct 2025).