Vague graphs has found its importance in most recent years. It has played the vital role in many real life applications. The mathematical approach of blending different aspects of vague graphs gives a more generalized approach. As a result of it, we introduce the concepts of Complex vague graphs (CVG). In this chapter, we introduce certain notions including union, join, complement and composition of complex vague graphs. This helps in manipulating the real life applications in decision making problems. We also investigate on the ideas of homomorphisms of complex vague graphs. Finally we provide an application of CVG in launching a water reservoir in different locations.
