This paper presented a new method of modeling a Software Defined Networking (SDN) network as a graph and importing traffic data into the created graph using graph techniques to speed up the computations required in traffic analysis and management. For this purpose, a specialized application named TMTA (Topology Modeling and Traffic Analysis) is created to model the SDN network topology as a graph and feed the created graph with traffic data. To achieve high performance, the TMTA application is integrated with the Neo4j graph database utilizing its ability to store and process big graphs consisting of massive amounts of highly interconnected data in a scalable and reliable manner. For performance evaluation, various sizes of network topologies ranging from 41 to 62,586 devices are modeled using the TMTA application and stored in Neo4j. Evaluation results show that the proposed big graph framework can handle large-scale topologies effectively and perform traffic analysis tasks, i.e., calculating the control score of each device in the network and finding the shortest path between devices in a very reasonable time.