Abstract
The main purpose of this paper is to introduce some connectivity concepts in the vague graphs. Connectivity concepts are the key in the graph clustering and networks. Also, they are the most important concept in the entire graph theory. Analogous to fuzzy cutvertices and fuzzy bridges in fuzzy graphs, vague cutvertices and vague bridges are introduced and characterized. We also proposed the concepts of gain and loss for paths and pairs of vertices. Connectivity in complete vague graphs is discussed and several types of arcs in the vague graphs are introduced. Finally, we gave an application of vague influence graph.
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