The fuzzy c-medoids algorithm (FCMdd) and robust fuzzy c-medoid algorithm (RFCMdd) [16] are used in clustering relational data. In this paper, we have modified FCMdd (mFCMdd) and also modified RFCMdd (mRFCMdd) by introducing a similarity relation comparing with the Cn graph to make FCMdd and RFCMdd algorithms useful for cluster cyclic networks. These algorithms are based on the graph distance of object to object, where the number of edges in the shortest path between two objects is considered as a measure of dissimilarity. We have also added applications to mFCMdd and mRFCMdd.