We study the discrete version of the p-Laplacian. Based on its variational
properties we discuss some features of the associated parabolic problem. Our
approach allows us in turn to obtain interesting information about positivity
and comparison principles as well as compatibility with the symmetries of the
graph. We conclude briefly discussing the variational properties of a handful
of nonlinear generalized Laplacians appearing in different parabolic equations.Comment: 35 pages several corrections and enhancements in comparison to the v
