Data analysis, data management, and big data play a major role in both social and business perspective, in the last decade. Nowadays, the graph database is the hottest and trending research topic. A graph database is preferred to deal with the dynamic and complex relationships in connected data and offer better results. Every data element is represented as a node. For example, in social media site, a person is represented as a node, and its properties name, age, likes, and dislikes, etc and the nodes are connected with the relationships via edges. Use of graph database is expected to be beneficial in business, and social networking sites that generate huge unstructured data as that Big Data requires proper and efficient computational techniques to handle with. This paper reviews the existing graph data computational techniques and the research work, to offer the future research line up in graph database management.