There is an increasing demand for a computer graphics - oriented software package for graph theory teaching and research. G-Net, a department research project headed by Dr. Kunwarjit Bagga, is an effort to create a computer software that contains a graph theory database, a graph editor, and a collection of algorithms to be executed on the graphs. This thesis concentrates on the design and implementation of a graph editor - GrapliPerfect. Graphs have been widely used to model many other phenomena. In this thesis, computer generated graphics images are used to represent graphs. This modeling relation between graphs and graphics is analyzed, and its role in the design and implementation of GraphPerfect is discussed in the thesis. To enhance the friendliness of the user interface, a simplified window system is presented.