An ancestral graph is a graph with three types of edges: directed edge, bidirected edge, and undirected edge such that it can be decomposed into three parts: an undirected subgraph, a directed subgraph, and directed edges pointing from the undirected subgraph to the directed subgraph.

An ancestral graph G over nodes V is maximal if for every pair (x, y) of non-adjacent nodes in G, there exists a set Z of nodes in V \{x, y} such that x and y are m-separated by Z in G.

In statistics, an ancestral graph can be used to represent the statistical dependencies, and notional causative effects, between random variables.

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