A classification of finite partial linear spaces with a primitive rank 3 automorphism group of almost simple type

A partial linear space is a non-empty set of points, provided with a collection of subsets called lines such that any pair of points is contained in at most one line and every line contains at least two points. Graphs and linear spaces are particular cases of partial linear spaces. A partial linear space which is not a graph or a linear space is called proper. In this paper, we give a complete classification of all finite proper partial linear spaces admitting a primitive rank 3 automorphism group of almost simple type.