Studies on the Structure and Dynamics of Urban Bus Networks in Indian Cities

TL;DR

This paper analyzes the structural properties and dynamics of urban bus networks in Indian cities using network science, revealing small-world features, topological diversity, and the impact of physical constraints on their evolution.

Contribution

It provides a comprehensive empirical analysis of Indian bus networks, highlighting their complex topologies, growth patterns, and the effects of physical constraints on their development.

Findings

Bus networks exhibit small-world properties and heavy-tailed degree distributions.

A wide spectrum of network topologies arises from preferential and random attachment.

Physical constraints influence the fractal dimensions and evolution of bus networks.

Abstract

In recent times, the domain of network science has become extremely useful in understanding the underlying structure of various real-world networks and to answer non-trivial questions regarding them. In this study, we rigourously analyze the statistical properties of the bus networks of six major Indian cities as graphs in L- and P-space, using tools from network science. Although public transport networks, such as airline and railway networks have been extensively studied, a comprehensive study on the structure and growth of bus networks is lacking. In India, where bus networks play an important role in day-to-day commutation, it is of significant interest to analyze their topological structure, and answer some of the basic questions on their evolution, growth, robustness and resiliency. We start from an empirical analysis of these networks, and determine their principle characteristics in terms of the complex network theory. The common features of small-world property and heavy tails in degree-distribution plots are observed in all the networks studied. Our analysis further reveals a wide spectrum of network topologies arising due to an interplay between preferential and random attachment of nodes. Unlike real-world networks, like the Internet, WWW and airline, which are virtual, bus networks are physically constrained in two-dimensional space by the underlying road networks. In order to understand the role of constraints in the evolution of these networks, we calculate their fractal dimensions that reveal a three-dimensional space-like evolution in a constrained two-dimensional plane. We also extend our study to understand the complex dynamical processes of epidemic outbreaks and information diffusion in these networks using SI and SIR models.