Graph theory, a branch of Mathematics plays a vital rule in studying interdisciplinary subjects such as physics, Chemistry, Engineering etc. Study of the properties of electrical circuits with the help of graph theory is a growing trend in mathematical and electrical fields. Electrical circuits consists of nodes and branches which obeys Kirchhoff ’s current laws, Kirchhoff ’s voltage laws etc. There are various well known theorems such as Norton’s theorem, Thevenin’s theorem, Superposition theorem, Millman Theorem etc for network analysis. In this paper, we try to analyze Millman’s theorem with the help of Graph theorem.