The Power Method algorithm is one of the simplest iterative approaches for determining the dominant eigenvector of matrices and graphs used in machine learning problems and it relies on Vector-Matrix-Multiplications (VMM). Recently, efficiency of the memristor crossbars in solving VMMs have been demonstrated using fundamental laws of the circuit theory. In this paper, we are proposing an analog circuit level implementation of the Power Method algorithm using memristor crossbars. It is found out that memristor based implementation provides more than an order of magnitude energy efficiency compared to the conventional digital systems.