Structure and robustness of Sao Paulo public transport network

Public Transport Networks plays a central role in cities devolopment. In big cities such system may be represented by a complex network and understand its properties is of great interest for managers and scholars. In this work, the urban public transport system of S\~ao Paulo is reinterpreted as a coupled (bus, subway and train) network, bypassing operational details and focusing on connectivity. Using a empirically generated graph, a statistical characterization is made by network metrics. Nearby bus stops and rail transport stations (subway and train) may or may not be considered as a single vertex in the network representation of the transport system, depending on how much an user is willing to walk to shift from one stop/station to another. This distance radius is then used to group nearby stops/stations as a single vertex in the network representation of the urban public transport system and then its properties are studied as a function of this radius. This radius is used as proxy of the user's willingness to walk until the nearest point to access transportation. The variation of the measure $ \rho $ leads to changes in the perception of the topology of the public transport network as shown in this work. An interesting result was that the network is assortative. Another aspect investigated was the degree distribution of the network. It was not possible to distinguish between power-law or a log-normal distribution. An exploratory model is used to test the robustness of the network by randomly, deterministically and preferentially targeting the stops and service lines. According to the grouping radius, aka willingness, different fragmentation values were obtained under attack simulations. We showed that increasing this willingness generates great reduction in the number of necessary jumps between buses, subway and trains lines to achieve all the network destinations.