Fig. 3

Spatial behavior of congestion nodes for the random planar models introduced in “A model for center-periphery entanglement” section with \(N=6000\), \(L=60\), and \(R^{(DT)}=24\). In the left panel, the resulting network configuration, with MST and DT edges painted in red and black, respectively. Hexagonal bins provide information about the occurrence of congestion nodes in space, and their colors show the related frequency in proportion to the intensity. In the right panel, we present the dependence of the congestion radius \(R_c\) on the patch radial size \(R_p\), i.e., the radius of the circle centered in the middle of the network, that is used to define the considered subgraph within this radius. The congestion radius range is divided in bins, and each point is located at the statistical mode \(R^*_c\) obtained with the distribution of \(R_c\) after 100 realizations. The color of the circular markers shows the probability of that value over the experimental \(R_c\) distribution. Shadow areas represent the variance of the different realizations of \(R_c\) values with respect to the bin average value