In this paper, some types of vague graphs are introdaced such as dm-regular, tdm-regular, m-highly irregular and m-highly totally irregular vague graphs are introduced and some properties of them are discussed. Comparative study between dm-regular (m-highly irregular) vague graph and tdm-regular (m-highly totally irregular) vague graph are done. In addition, dm-regularity and m-highly irregularity on some vague graphs, which underlying crisp graphs are a cycle or a path is also studied. Finally, some applications of regular vague graphs are given for demonstration of fullerene molecules, road transport network and wireless multihop networks.