An important application of graph partitioning is data clustering using a graph model - the pairwise similarities between all data objects form a weighted graph adjacency matrix that contains all necessary information for clustering. Here we propose a new algorithm for graph partition with an objective function that follows the min-max clustering principle. The relaxed version of the optimization of the min-max cut objective function leads to the Fiedler vector in spectral graph partition. Theoretical analyses of min-max cut indicate that it leads to balanced partitions, and lower bonds are derived. The min-max cut algorithm is tested on news-group datasets and is found to outperform other current popular partitioning/clustering methods. The linkage-based refinements in the algorithm further improve the quality of clustering substantially. We also demonstrate that the linearized search order based on linkage differential is better than that based on the Fiedler vector, providing another effective partition method.