Conceptual Neighborhoods of Topological Relations Between Lines

Conceptual neighborhood graphs capture the similarity among qualitative relations. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundary lines, roughly at the same degree as it increases for crisp lines that are transformed from R into R.