“…On the one hand, we note that in the literature, one can find some works about nonlinear filters on graphs and hypergraphs, particularly mathematical morphology operators in the algebraic sense [3,4,5,6,7,8,9], where the couple of nonlinear operator (dilation/erosion) are maps from two different lattices, i.e., they are maps "from nodes to edges" or "edges to nodes". On the other hand, some regularisation techniques and nonlinear operators have been introduced on function evaluated on graph via directional derivative [10] [11] [12] or discrete version of the p-Laplacian [13].…”