Determine the convergence rate of the normalized largest signless p-Laplacian eigenvalue

Determine the convergence rate, as p tends to infinity, of the normalized largest signless p-Laplacian eigenvalue $\lambda^{(p)}_{\max}(G)/2^p$ for a weighted graph $G=(V,E,w,\mu,\kappa)$.

Background

The paper cites the known convergence of $\lambda^{(p)}_{\max}(G)/2^p$ to the largest eigenvalue of the adjacency matrix as p tends to infinity. While numerical experiments illustrate this limiting behavior, the rate at which the normalized eigenvalue approaches its limit is left undetermined for a general weighted graph with vertex measures and potential function.