Abstarct: The graphs modeling is the use of concepts, relationships, and graphs structure on the problems of modeling. In this thesis, the fuzzy modeling of graphs, baxsed on the fuzzy graph types, including the fuzzy trees, fuzzy Euler and Hamiltonian graphs, fuzzy planar graphs, fuzzy bipartite graphs, fuzzy networks and the problems such as the fuzzy coloring, fuzzy vertex cover, and the fuzzy independent sets are discussed. Also for each the graph model, the examples are expressed, Then solutions and applications of the graph model are presented.