Matrix representation of double layered complete fuzzy graph

In this paper, we have defined a new matrix representation using edge membership values of the complete fuzzy graph. Uncertainties in a problem are represented as fuzzy matrices using fuzzy principles. Recent days fuzzy matrices have become very famous. In this paper unlike the usual matrix representation of a fuzzy graph with respect to vertices, a new matrix representation with edge membership values as rows and columns is introduced. The relationship between the double layered complete fuzzy graph and the given fuzzy graph whose crisp graph is a complete are analyzed.