Public transport network analysis

At least once in a lifetime, everyone has taken a means of public transport. Buses, subways, trains, etc., are a part of our everyday life. They are how we commute to work, meet a friend for a coffee and visit or travel to different places. In the last decades, researches have studied the topology and characteristics of Public Transport Networks (PTN) in order to understand, plan and optimize their behaviour, cost and performance. In particular, when dealing with spatial networks such as PTNs, complex network theory plays a huge role in analysing and understanding their properties. In this thesis, we focus on the PTNs analysis of 27 cities located in three continents: Europe (19), Oceania (5) and America (3). We model each transportation network as a graph represented by a \textit{L-space} topology, where stops and stations represent nodes and their connections, e.g. a bus going from stop A to stop B, edges. This work aims at finding possible relations/patterns involving the city features, such as area and population, and the properties of its PTN. We collect basic static measurements, for each city, such as the number of nodes and edges, clustering coefficient, density and diameter. We deepen the network analysis discussing assortativity and average path length. We further explore the properties of each network through the distributions of nodes measures, like degree and different types of centrality. We then explore the networks in order to analyse shortest paths and distances, computed by standard graph algorithms and evaluated taking into account euclidean distances. This allows us to partially capture some geographical, topological and functional characteristics of the observed networks. We conclude our work with frequency analysis. The goal is to display and analyse the distributions of the number of vehicles throughout a typical day. The work is done separately for each type of transport present in the dataset, which allows to better compare the situation in different cities. We use local as well as global features to evaluate characteristics of urban transportation systems according to well-known network theory, e.g. small-world and scale-free properties. We make local and global analysis on individual and multiple urban networks, considering their basic topology as well as clustering strategies based on commonly used properties. Each analysis has its own level of details, depending on the type of measure taken into consideration. For example, in some cases, it is possible to have both city-level analysis and comparison among cities for all measures considered, whereas other times it is necessary to divide by type of measurement. The results obtained from the network analysis suggest that PTNs, like many other real-world networks, are neither small-world nor scale-free. Lastly, for each of the part of the analysis performed we were able to capture some insights both at the city level as well as in terms of comparisons among all cities.