Abstract
Fuzzy graph is a graph consists pair of vertex and edge that have degree of membership containing closed interval of real number [0,1] on each node and edge. A graph fuzzy is connected if the strength of connectedness between nodes u and v larger than zero for each . This paper will be explained about ss-path and ss-distance. Strongest stong path (ss-path) between two nodes in connected fuzzy graph if path is a strongest path as well as strong path. If G is a connected fuzzy graph then for each there exists a strongest strong path for u to v . While ss-distane between two nodes u and v in connected fuzzy graph as the reciprocal of the strength of connectedness between nodes u and v. Using metric can be known that every connected fuzzy graph is ss-selfcentered