In Social Graph, a set of entities or nodes or vertices interact with each other in a complicated manner that can form multiple types of relationships that depend on time and types of complications. Such graphs include multiple subsystems and layers of connectivity. So it is important to take such multi-layer features into account to make easier of understanding of such complex systems. In this paper, the author focuses on a Social Graph to represent in a multi-layer graph based on its characteristics lies in each node or vertex or entity. For this, the author proposes a general model related to Social Graph. For this model, the author proposes an algorithm, SoGraM for representation of Social Graph with multi-layer features using Graph Mining Techniques. Further, the author tries to prove the proposed algorithm with three examples of Social Graph namely Author Graph, Email Graph, and Telephone Graph.