Abstract
Fuzzy models are becoming useful because of their aim of reducing the differences between the traditional numerical models used in engineering and sciences and the symbolic models used in expert systems. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce various types of vague bridges, vague cut-vertices, vague cycles and vague trees in vague graphs, and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.