parents of . Therefore, an edge between them is added. According to the new order, the second node that is considered is . This node has only one parent (). Therefore, no new edge is added. The third considered node is . Its only parent is . Indeed, and are not joined this time. As a result, no new edge is introduced. Since has no parent as well, the final induced graph is the one above. This induced graph differs from the one produced by the previous ordering. See also Directed graph Local consistency References Constraint programming Extensions and generalizations of graphs