Some properties of vague graphs with application

Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. The vague graphs are more flexible and compatible than fuzzy graphs due to the fact that they have many applications in networks. In this paper, busy vertices, free vertices, strong arc, busy value, isolated vertex, fully free vertex and partial free vertex in vague graphs are defined. Likewise, some interesting properties of isomorphism and weak isomorphism on them are introduced. Finally, we give an application of vague digraph in vulnerability assessment of gas pipeline networks.