Main panel, the eigenvalue , equation (92) in Supplementary Information for the two-body interaction ℓ = 1, obtained by minimizing the energy function with the RS cavity method. The curve was computed on an ER graph of N = 10,000 nodes and average degree 〈k〉 = 3.5 and then averaged over 40 realizations of the network (error bars are s.e.m.). Inset, comparison between the RS cavity method and EO (extremal optimization) for an ER graph of 〈k〉 = 3.5 and N = 128. The curves are averaged over 200 realizations (error bars are s.e.m.).