Vague graph represents the systems with uncertainty perfectly. In this paper, we introduced the strengths of paths in vague graphs. Different types of strong edges are discussed with examples. A new concept of strong edges, namely, independent strong edges is defined. The condition of vertex membership values of a complete vague graph such that all the edges are independent strong edge, is established. After that, strong vertex, vertex connectivity, edge connectivity of vague graphs are introduced. The relation between edge connectivity and independent strong edge is established. Besides, several properties of the stated graphs have been proved.
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