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In this paper we study numerical approximations of the evolution problem forthe nonlocal $p$-Laplacian operator with homogeneous Neumann boundaryconditions on inhomogeneous random convergent graph sequences. More precisely,for networks on convergent inhomogeneous random graph sequences (generatedfirst by deterministic and then random node sequences), we establish theircontinuum limits and provide rate of convergence of solutions for the discretemodels to their continuum counterparts as the number of vertices grows. Ourbounds reveals the role of the different parameters, and in particular that of$p$ and the geometry/regularity of the data.

Continuum limit of the nonlocal p-Laplacian evolution problem on random inhomogeneous graphs