The avalanche-size exponent, τ, and the avalanche-dimension, D, for networks with nodes’ out-degrees drawn from a Gausssian distribution with a fixed mean coordination number μ = 4, and standard deviations σ = 0, 1, 2.

Note that the case of σ = 0 is just a randomly rewired version of the regular lattice with coordination number K = 4, see Fig 3(b) for the data collapse. Within error bars, both scaling exponents are consistent with the mean-field model τ = 3/2 and D = 2.