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Fig. 5 | Applied Network Science

Fig. 5

From: Emergence of spatial transitions in urban congestion dynamics

Fig. 5

Congestion radius pattern for the setup introduced in Sec. 5, with \(N=3000\), \(L=20\), \(R^{(DT)}=5\), and \(\Delta =10\). Hybrid region is generated by overlapping a fraction \(\pi =0.5\) of DT edges sampled from the distribution in Eq. (2), with \(k=0.1\). In the left panel, the blue histogram describes the final distribution of these edges. The right panel reports the congestion radius \(R_c\) as a function of the parch radius \(R_p\). The black and purple dashed line report the result related to \(\pi =1\) and \(\pi =0.05\) respectively, where all the edges and approximately no one have been added, and match the situation described in Sec. 4. The dotted line refers to the edge distribution shown in the right panel, where circles are located at the statistical mode over an ensemble of 100 realizations. In this case transition exhibits a smooth, rather than abrupt, profile as a consequence of the non-tight discontinuity in the edge density

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