Abstract: The concept of connective degree is utilized for the identification of topological difference in the geometric structure of a line,its generally topological definition of a line is given.A generic model,called the 4-intersection-and-difference,is set up for the description of basic line-line topological relations,upon which a conceptual neighborhood graph is built with the consideration of topological distance.It concludes that the proposed model in this paper can represent the property of topological changes,and basic relations between line segments in IR~1 and IR~2.