Distribution of neighborhood size in cities

TL;DR

This paper investigates the distribution of neighborhood sizes in 12 global cities, revealing an exponential decay pattern that aligns with city size distributions and is explained through a wealth-mediated migration model.

Contribution

It introduces a wealth-based model of neighborhood dynamics that explains the exponential distribution of neighborhood sizes observed across multiple cities.

Findings

Neighborhood sizes follow exponential decay in all studied cities.

The model reproduces exponential decay under various parameters.

Wealth and affordability thresholds are key to the distribution's emergence.

Abstract

We study the distribution of neighborhoods across a set of 12 global cities and find that the distribution of neighborhood sizes follows exponential decay across all cities under consideration. We are able to analytically show that this exponential distribution of neighbourhood sizes is consistent with the observed Zipf's Law for city sizes. We attempt to explain the emergence of exponential decay in neighbourhood size using a model of neighborhood dynamics where migration into and movement within the city are mediated by wealth. We find that, as observed empirically, the model generates exponential decay in neighborhood size distributions for a range of parameter specifications. The use of a comparative wealth-based metric to assess the relative attractiveness of a neighborhood combined with a stringent affordability threshold in mediating movement within the city are found to be necessary conditions for the the emergence of the exponential distribution. While an analytical treatment is difficult due to the globally coupled dynamics, we use a simple two-neighbourhood system to illustrate the precise dynamics yielding equilibrium non-equal neighborhood size distributions.