Empirical analysis and modeling of urban public transport network of Sao Paulo

Every complex system has an inherent network that represent the structural relationship between its elements, and a convenient way to interpret this interaction is through the graph theory. In this work, the urban public transport network of Sao Paulo is reinterpreted as a complex network, abstracting its operational details and focusing on connectivity. Using the resulted graph, a characterisation of the statistical properties of the network is performed. Further, we propose a model that permit to simulate the network vulnerabilities, with the purpose to get a topology and structure that increases the robustness. The node degree distribution shows evidence of scale-free phenomenon, while the average length of paths indicates the small-world property. These findings support two main characteristics observed in the literature such networks: they have a high rate of robustness under random failure but are vulnerable to targeted attacks on important nodes or links.