Modeling Metropolis Public Transport

TL;DR

This paper surveys major city public transport networks, analyzes their structural properties, and introduces an evolutionary model based on self-avoiding walks that replicates key network features.

Contribution

It provides a comprehensive analysis of PTN structures and proposes a novel evolutionary growth model based on self-avoiding walks that captures their key properties.

Findings

PTNs exhibit unique geographical and network properties.

Self-avoiding walk behavior relates to surface coverage optimization.

The proposed model successfully reproduces real PTN features.

Abstract

We present results of a survey of public transport networks (PTNs) of selected 14 major cities of the world with PTN sizes ranging between 2000 and 46000 stations and develop an evolutionary model of these networks. The structure of these PTNs is revealed in terms of a set of neighbourhood relations both for the routes and the stations. The networks defined in this way display distinguishing properties due to the constraints of the embedding 2D geographical space and the structure of the cities. In addition to the standard characteristics of complex networks like the number of nearest neighbours, mean path length, and clustering we observe features specific to PTNs. While other networks with real-world links like cables or neurons embedded in two or three dimensions often show similar behavior, these can be studied in detail in our present case. Geographical data for the routes reveal surprising self-avoiding walk properties that we relate to the optimization of surface coverage. We propose and simulate an evolutionary growth model based on effectively interacting self-avoiding walks that reproduces the key features of PTN.