Fig. 4: Asymptotics of the ϕ-norm in the geometric renormalization of weights (GRW).
The renormalized weight \({\omega }^{{\prime} }(\phi =1)\) and \({\omega }^{{\prime} }(\phi =\infty )\) versus \({\omega }^{{\prime} }({\phi }^{* })\), where ϕ* is the inferred value ϕ* = β/(η − 1 + α), for different number of links E between the constituent nodes of two supernodes are displayed in (a–c) for Openflights and in (d–f) for Collaboration. Note that when r = 2, the number of links E can have values 1, 2, 3 or 4, and that sum-GRW corresponds to the case ϕ = 1 while sup-GRW to ϕ = ∞. We used the sets {ωmn} following the coarse-graining in the real network, and performed an iteration of ϕ − GRW to calculate the renormalized weight \({\omega }^{{\prime} }\) with Eq. (3).
