M. R. Anderberg (1973) and B. S. Everitt (1993) have developed the cluster Analysis which is a process to decompose the set of objects from a finite set into subgroups or clusters based on similarity. Crisp clustering techniques are classified into 3 groups according to the algorithmic approach as (i) Hierarchical clustering method (ii) Graph-Theoretic clustering method (iii) Objective function based clustering method. Graph-theoretic clustering methods are normally based on some kind of connectivity of the nodes of a graph representing the data set. The fuzzy graph approach is more powerful in cluster analysis than the usual graph-theoretic approach. The concept of fuzzy graph with edges associated with two types of weights were studied before⁹. In this study a min-max weight of the cut set and min-max edge connectivity are introduced. The clustering technique of narrow slicing procedure² based on edge connectivity has been adopted for determining -edge components of a fuzzy graph.