Recent years have seen an explosion in graph data from a variety of scientific, social and technological fields. From these fields, emotion recognition is an interesting research area because it finds many applications in real life such as in effective social robotics to increase the interactivity of the robot with human, driver safety during driving, pain monitoring during surgery etc. A novel facial emotion recognition based on graph mining has been proposed in this paper to make a paradigm shift in the way of representing the face region, where the face region is represented as a graph of nodes and edges and the gSpan frequent sub-graphs mining algorithm is used to find the frequent sub-structures in the graph database of each emotion. To reduce the number of generated sub-graphs, overlap ratio metric is utilized for this purpose. After encoding the final selected sub-graphs, binary classification is then applied to classify the emotion of the queried input facial image using six levels of classification. Binary cat swarm intelligence is applied within each level of classification to select proper sub-graphs that give the highest accuracy in that level. Different experiments have been conducted using Surrey Audio-Visual Expressed Emotion (SAVEE) database and the final system accuracy was 90.00%. The results show significant accuracy improvements (about 2%) by the proposed system in comparison to current published works in SAVEE database.