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An ordered graph is a graph with a total order over its nodes.
In an ordered graph, the parents of a node are the nodes that are adjacent to it and precede it in the ordering. More precisely, n {\displaystyle n} is a parent of m {\displaystyle m} in the ordered graph ⟨ N , E , < ⟩ {\displaystyle \langle N,E,<\rangle } if ∈ E {\displaystyle \in E} and n < m {\displaystyle n The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node. In particular, nodes are considered in turn according to the ordering, from last to first. For each node, if two of its parents are not joined by an edge, that edge is added. In other words, when considering node n {\displaystyle n} , if both m {\displaystyle m} and l {\displaystyle l} are parents of it and are not joined by an edge, the edge {\displaystyle } is added to the graph. Since the parents of a node are always connected with each other, the induced graph is always chordal.