Sorting is a well-known problem frequently used in many aspects of the world of computational applications. Sorting means arranging a set of records (or a list of keys) in some (increasing or decreasing) order. In this paper, we propose a graph based comparison sorting algorithm, designated as RKPianGraphSort, that takes time Θ(n²) in the worst-case, where n is the number of records in the given list to be sorted.