Graph cut, partitioning the vertices of a graph into two or more disjoint subsets, is a fundamental problem in graph theory and has become a very powerful tool in data clustering. In this talk, we first try to connect two kinds of graph cut: the Cheeger cut and the max cut, with continuous function optimization problems through the graph 1-Laplacian. That is, the original discrete combination optimization problems can be equivalently transformed into the continuous function optimization problems and then the nonlinear eigenvalue problems. Second, we discuss theory and algorithms for such nonlinear eigenvalue problems which are usually not only nonconvex but also nondifferentiable. Finally, some preliminary numerical results are provided.