Graph based Recommender models make use of user-item rating and user-user social relationships to elicit recommendation performance by extracting inherent geometrical knowledge. In a social graph scenario, user-user trust plays a significant role in reducing sparsity and has varied characteristics that can be exploited. Existing models limit themselves to learning from either a high order interaction graph of user-item ratings or a user-user social graph from trust value. They explore other trust characteristics in a very limited setting. The graph based model, designed using entire user-user social information, impacts performance and escalates complexities in model learning. To alleviate these issues of graph learning, graph recommender seeks assistance from matrix factorization techniques. Incorporating graph based model with matrix factorization brings its own set of challenges of model integration, leveraging trust, graph learning, and optimization. This article presents the existing work in that line and future possibilities and challenges to be catered to through novel developments