A graph, comprising a set of nodes connected by edges, is one of the simplest yet remarkably useful mathematical structures for the analysis of real-world complex systems. Network theory, being an application-based extension of graph theory, has been applied to a wide variety of real-world systems involving complex interconnection of subsystems. The application of network theory has permitted in-depth understanding of connectivity, topologies, and operations of many practical networked systems as well as the roles that various parameters play in determining the performance of such systems. In the field of transportation networks, however, the use of graph theory has been relatively much less explored, and this motivates us to bring together the recent development in the field of public transport analysis from a graph theoretic perspective. In this paper, we focus on ground transportation, and in particular the bus transport network (BTN) and metro transport network (MTN), since the two types of networks are widely used by the public and their performances have significant impact to people's life. In the course of our analysis, various network parameters are introduced to probe into the impact of topologies and their relative merits and demerits in transportation. The various local and global properties evaluated as part of the topological analysis provide a common platform to comprehend and decipher the inherent network features that are partly encoded in their topological properties. Overall, this paper gives a detailed exposition of recent development in the use of graph theory in public transport network analysis, and summarizes the key results that offer important insights for government agencies and public transport system operators to plan, design, and optimize future public transport networks in order to achieve more efficient and robust services.