Theoretical concepts of graphs are highly utilized by computer scientists. Especially in research areas of computer science such as data mining, image segmentation, clustering image capturing, networking, etc. The cubic vague graphs are more flexible and compatible than fuzzy graphs due to the fact that they have many applications in networks. In this paper we have introduced the notion of cubic vague graph which extends the notion of cubic graph as well as vague graph. The novelty and significance of new concept is demonstrated with the help of examples. We have developed many operations on cubic vague graphs such as the union, join, cartesian product, and the composition. Also, we defined self complementary cubic vague graph and studied its properties. Finally an application of cubic vague influence graph in a social group is given.
