Diffusion and synchronization dynamics reveal the multi-scale patterns of spatial segregation

TL;DR

This paper introduces a novel approach using diffusion and synchronization dynamics to analyze multi-scale spatial segregation patterns in urban socioeconomic distributions, revealing how deprivation and affluence influence segregation levels.

Contribution

It develops a method to quantify spatial heterogeneity of socioeconomic features through diffusion and synchronization times, capturing complex multi-scale segregation patterns.

Findings

Deprivation and affluence areas show higher diffusion and synchronization times.

The method detects neighborhoods with steeper segregation.

It provides a dynamic perspective on spatial heterogeneity.

Abstract

Urban systems are characterized by populations with heterogeneous characteristics, and whose spatial distribution is crucial to understand inequalities in life expectancy or education level. Traditional studies on spatial segregation indicators focus often on first-neighbour correlations but fail to capture complex multi-scale patterns. In this work, we aim at characterizing the spatial distribution heterogeneity of socioeconomic features through diffusion and synchronization dynamics. In particular, we use the time needed to reach the synchronization as a proxy for the spatial heterogeneity of a socioeconomic feature, as for example, the income. Our analysis for 16~income categories in cities from the United States reveals that the spatial distribution of the most deprived and affluent citizens leads to higher diffusion and synchronization times. By measuring the time needed for a neighborhood to reach the global phase we are able to detect those that suffer from a steeper segregation. Overall, the present manuscript exemplifies how diffusion and synchronization dynamics can be used to assess the heterogeneity in the presence of node information.