Fig. 9

Comparison of different weight models at the example of marginal node resolvent-based subgraph centralities of Stuttgart. Central stops are marked red and non-central stops are marked blue. The subcaptions denote the respective intra-layer weights \([\varvec{A}^{(l)}]_{ij}\) in the case that nodes i and j are connected in layer l. Otherwise, \([\varvec{A}^{(l)}]_{ij}\) is set to 0 in all cases. The plots in the first column are obtained without frequencies, whereas the plots in the second column are obtained with frequencies. The plots in the first row are obtained without a Gaussian kernel applied to travel times, whereas the plots in the second row are obtained with a Gaussian kernel applied to travel times. Furthermore, the same Gaussian kernel is also applied to inter-layer transfer times in the second row. The parameters are chosen as \(\alpha =0.5/\lambda _{\mathrm {max}}\), \(\sigma =5\), and \(\Delta t_{\mathrm {transfer}}=5\). The street network in the background of the plots is created with the OSMnx python package (Boeing 2017)