The uniform Lp and L∞ estimates established for nonlocal and graph Poisson equations have significant implications for the analysis and solution of these equations. These estimates provide bounds on the solutions and gradients of the equations, ensuring the stability and convergence of numerical methods used to solve them. The Lp estimates guarantee the existence of solutions in appropriate function spaces, while the L∞ estimates ensure the boundedness of solutions, which is crucial for practical applications. Additionally, these estimates play a key role in proving the convergence of solutions as the number of data points approaches infinity, leading to a better understanding of the continuum limit behavior of the equations on graphs.