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Urban mobility forecast and analysis can be addressed through grid-based andgraph-based models. However, graph-based representations have the advantage ofmore realistically depicting the mobility networks and being more robust sincethey allow the implementation of Graph Theory machinery, enhancing the analysisand visualisation of mobility flows. We define two types of mobility graphs:Region Adjacency graphs and Origin-Destination graphs. Several node centralitymetrics of graphs are applied to identify the most relevant nodes of thenetwork in terms of graph connectivity. Additionally, the Perron vectorassociated with a strongly connected graph is applied to define a circulationfunction on the mobility graph. Such node values are visualised in thegeographically embedded graphs, showing clustering patterns within the network.Since mobility graphs can be directed or undirected, we define several GraphLaplacian for both cases and show that these matrices and their spectralproperties provide insightful information for network analysis. The computationof node centrality metrics and Perron-induced circulation functions for threedifferent geographical regions demonstrate that basic elements from GraphTheory applied to mobility networks can lead to structure analysis for graphsof different connectivity, size, and orientation properties.

Graph-Based Analysis and Visualisation of Mobility Data