The dimensionality of mixed ancestral graphs
First we will introduce some graph terminology. The concepts defined here are illustrated in Figure 1. A graph consists of two parts, a set of vertices V and a set of edges E. Each edge in E is between two distinct vertices in V. There are two kinds of edges in E, directed edges A → B or A ← B, and double-headed edges A ↔ B; in either case A and B are endpoints of the edge; further, A and B are said to be adjacent. In Figure 1 the set of vertices is {A,B,C,D,E} and the set of edges is {A ↔ B, B → C, C → D, E → D}. For a directed edge A → B, A is the tail of the edge and B is the head of the edge, A is a parent of B, and B is a child of A.