Generalized β-skeletons

β-skeletons, a prominent member of the neighborhood graph family, have interesting geometric properties and various applications ranging from geographic networks to archeology. This paper focuses on developing a new, more general than the present one, definition of β-skeletons based only on the distance criterion. It allows us to consider them in many different cases, e.g. for weighted graphs or objects other than points. Two types of β-skeletons are especially well-known: the Gabriel Graph (for β = 1) and the Relative Neighborhood Graph (for β = 2). The new definition retains relations between those graphs and the other well-known ones (minimum spanning tree and Delaunay triangulation). We also show several new algorithms finding β-skeletons.