  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.
