Fig. 2. Real on-road public transportation (PT) networks.

a, b The network representation of the PT system with color-coded link qualities q at t = 8 (8:00 A.M.), for Melbourne on 1 September 2017 (a), and for Brisbane on 1 March 2013 (b). c Percolation process on Melbourne’s network shown in (a). The size of the giant component ∣GC∣ and the size of the second-largest component ∣SC∣ are plotted as functions of the threshold ρ. The critical threshold ρ = ρ_c is determined as the point of maximal ∣SC∣ (vertical dashed gray line). d Percolation process on Melbourne’s network shown in (a). Unaffected demand is plotted as a function of ρ (UD_ρ) which at percolation critical threshold shows the value of ${\mathrm{UD}}_{{\rho }_c}\approx 0.8$ (marked by dashed gray lines). The area hatched in red corresponds to the reliability α of the network in (a). Streetmap layers in a and b ©OpenStreetMap contributors⁴⁴.