In this outlet, a journey amid three models are designed. Graphs, fuzzy graphs and neutrosophic graphs are three models which form main parts. Assigning one specific number with some conditions to vertices and edges of graphs make them to be titled as fuzzy graphs and assigning three specific numbers with some conditions to vertices and edges of graphs make them to be titled as neutrosophic graphs. In other viewpoint, neutrosophic graphs are 3-array fuzzy graphs which every things are triple. To make more sense, the well-known graphs are defined in new ways. For example, crisp complete, fuzzy complete and neutrosophic complete when the context is about being complete in every model. New notions are defined in the comparable structures on these three models to understand the behaviors of these models according to the notions. New notions are defined in the comparable structures on these three models to understand the behaviors of these models according to the notions.