Figure 5: Comparison between theory and simulation.
From: Spatio-temporal propagation of cascading overload failures in spatially embedded networks
(a) Relative velocity as a function of tolerance in the theory, models as well as in real structures. The relative velocity is calculated in the linear regime of rc(t), Δ(rc)/L, which decreases with α. The velocity in the theory is multiplied by a constant 2π. We find that the velocity is similar in different model networks (lattice, circular lattice, planar graph and circular plate) and real networks (road networks in Oldenburg and California). (b) The average overload as a function of relative distance from the initial attack. The overload in the weighted lattice (circle symbol) and theory (dashed line) after the initial damage is shown. The results are both shifted by the linear size of the initial damage 
, which makes two results comparable from the initial attack. We also multiplied the x axis of theory by 2Ï€, which is consistent with the velocity difference shown in a.
