Vertical partitioning is the process of subdividing the attributes of a relation or a record type, creating fragments. Previous approaches have used an iterative binary partitioning method which is based on clustering algorithms and mathematical cost functions. In this paper, however, we propose a new vertical partitioning algorithm using a graphical technique. This algorithm starts from the attribute affinity matrix by considering it as a complete graph. Then, forming a linearly connected spanning tree, it generates all meaningful fragments simultaneously by considering a cycle as a fragment. We show its computational superiority. It provides a cleaner alternative without arbitrary objective functions and provides an improvement over our previous work on vertical partitioning.