Graph-Based Approximation and Analysis of Traffic Data on Mobility Networks

Urban mobility is a pillar in geographical systems and smart cities. The understanding of the parts and their interrelated movement within urban regions or city networks is essential for comprehending complex spatial dynamics and making informed decisions in urban planning and traffic control. The limitations of various mobility and traffic data collection methods make it challenging to explain movement across an entire area of interest, underscoring the need for methods to approximate values in uncovered zones. In addition, it has been recognised in the literature that spatial dynamics benefit significantly from graph-based layouts, as they can accurately model displacements among distant regions. For this reason, our approach is based on the modelling of urban systems as a graph, and the reconstruction of missing data is addressed by solving the graph signal recovery problem. This thesis proposes a unified graph-based framework for analysing urban mobility systems and reconstructing missing traffic data using real-world spatial and trajectory information. By modelling cities as graphs, where nodes represent road segments or administrative regions and edges capture physical or geographical relationships, the framework leverages Graph Signal Processing techniques to estimate unobserved traffic variables such as vehicle volume, average speed, and density. To address the challenges posed by sparse or incomplete datasets, the framework employs signal recovery methods based on spectral graph theory and adjacency structures. Graph signals are constructed using multimodal trajectory data, allowing for the approximation of traffic states on road networks. The accuracy of these reconstructions is evaluated using multiple error metrics that compare estimated values with available ground-truth data. The thesis introduces two core graph representations, road graphs and region adjacency graphs, as foundational models. Topological analysis is conducted using classical and adapted centrality measures to identify structurally critical zones across networks of varying scale and connectivity. In particular, several centrality metrics are tested to show areas of strategic importance in terms of mobility and access. A novel contribution of this work is the implementation of non-conventional node scores for region adjacency graphs. These scores incorporate spatial and mobility features commonly used in forecasting models, enabling structural insights that are typically overlooked in graph-based topological analysis. The results show that integrating such features significantly enhances the interpretability and utility of spatial network analysis. Another key innovation is the comparative evaluation of signal recovery performance on directed versus undirected road graphs, demonstrating the importance of accounting for directionality in urban traffic modelling. The methodology combines data processing, graph construction, signal projection, and visualisation techniques to deliver interpretable and actionable insights. Applied case studies validate the framework’s effectiveness in identifying mobility patterns, detecting traffic anomalies, and informing data-driven decisions for infrastructure planning, congestion mitigation, and urban policy development. Overall, this thesis offers a robust analytical toolset for advancing the understanding and management of complex urban mobility systems.