  We study Gamma-convergence of graph based Ginzburg-Landau functionals, both
the limit for zero diffusive interface parameter epsilon->0 and the limit for
infinite nodes in the graph m -> infinity. For general graphs we prove that in
the limit epsilon -> 0 the graph cut objective function is recovered. We show
that the continuum limit of this objective function on 4-regular graphs is
related to the total variation seminorm and compare it with the limit of the
discretized Ginzburg-Landau functional. For both functionals we also study the
simultaneous limit epsilon -> 0 and m -> infinity, by expressing epsilon as a
power of m and taking m -> infinity. Finally we investigate the continuum limit
for a nonlocal means type functional on a completely connected graph.
