In this paper, we present a graph-based fingerprint classification algorithm that deals with ones collected from touch scanners. A relational graph, which reflects distribution of ridge directions in an orientation field, is constructed with additional emphasis on the distribution of the ridges inside the core area that is defined to minimize external influences. For classification, a general edit distance scheme is employed to measure the similarity between the constructed graph and pre-trained graph models. Experimental results using a database in FVC2004 show that the proposed algorithm has higher classification accuracy than other structural approaches.