Shifted Eigenvector Models for Centrality and Occupancy in Urban Networks

TL;DR

This paper introduces shifted eigenvector models for urban network centrality that incorporate topological and non-topological factors, enabling assessment of urban interventions through fixed-point equations and sensitivity analysis.

Contribution

It develops a novel family of centrality models based on fixed-point equations, linking node occupancy and attraction, with methods for parameter estimation and impact assessment.

Findings

Models can estimate intrinsic attraction and occupancy from data

Framework enables evaluation of urban interventions

Explicit formulas facilitate sensitivity analysis

Abstract

This article investigates a family of centrality models for urban networks that incorporate both topological and non-topological factors. Since centrality is inherently recursive, these models can be formulated as fixed-point equations, which we refer to as shifted eigenproblems. Assuming a correlation between node centrality and occupancy, we discuss how experimental data can be used to estimate model parameters via least-squares methods. Furthermore, such data would allow us to infer the intrinsic attraction of each node, as well as the occupancy induced by must-visit points of interest, a task that is conceptually challenging. Once the model parameters are fitted and validated, our framework can be used to assess the impact of urban interventions, such as introducing a must-visit point of interest at a specific node or enhancing its intrinsic attraction. The resulting sensitivity analysis is therefore highly relevant for urban planning decisions. We also provide explicit formulas to facilitate this analysis.