Fuzzy graph (FG) models embrace the ubiquity of existing in natural and man-made structures, specifically dynamic processes in physical, biological, and social systems. It is exceedingly difficult for an expert to model those problems based on a FG because of the inconsistent and indeterminate information inherent in real-life problems being often uncertain. Vague graph (VG) can deal with the uncertainty associated with the inconsistent and determinate information of any real-world problem,

more »

... e FGs many fail to reveal satisfactory results. Regularity definitions have been of high significance in the network heterogeneity study, which have implications in networks found across biology, ecology, and economy; so, adjacency sequence (AS) and fundamental sequences (FS) of regular vague graphs (RVGs) are defined with examples. One essential and adequate prerequisite has been ascribed to a VG with maximum four vertices is that it should be regular based on the adjacency sequences concept. Likewise, it is described that if ζ and its principal crisp graph (CG) are regular, then all the nodes do not have to have the similar AS. In the following, we obtain a characterization of vague detour (VD) g-eccentric node, and the concepts of vague detour g-boundary nodes and vague detour g-interior nodes in a VG are examined. Finally, an application of vague detour g-distance in transportation systems is given.