The defect morphology is an essential aspect of the evolution of crystal microstructure and its response to stress. While reliable and efficient standard computational algorithms exist for finding defect concentration and size distribution in a crystal, defect morphology identification is still nascent. The need for an efficient and comprehensive algorithm to study defects is becoming more evident with the increase in the amount of simulation data and improvements in data-driven algorithms. We present a method to characterize a defect's morphology precisely by reducing the problem into graph theoretical concepts of finding connected components and cycles. The algorithm can identify the different homogenous components within a defect cluster having mixed morphology. We apply the method to classify morphologies of over a thousand point defect clusters formed in high energy W collision cascades. We highlight our method's comparative advantage for its completeness, computational speed, and quantitative details.