An empirical study is performed on the local-optimum space of graph bipartitioning. We examine some statistical features of the fitness landscape. They include the cost-distance correlations and the properties around the central area of local optima. The study revealed some new notable results about the properties of the fitness landscape; e.g., the central area yielded fairly good quality in the local-optimum space. We performed an experiment on a spectrum of different exploitation strengths of the central areas. From the results, it seems attractive to exploit the central area, but excessive or insufficient exploitation is not desirable.