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In graph theory, reachability refers to the ability to get from one vertex to another within a graph. We say that a vertex can reach a vertex (or that is reachable from ) if there exists a sequence of adjacent vertices (i.e. a path) which starts with and ends with . In an undirected graph, it is sufficient to identify the connected components, as any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component. The connected components of a graph can be identified in linear time. The remainder of this article focuses on reachability in a ''directed'' graph setting. == Definition == For a directed graph , with vertex set and edge set , the reachability relation of is the transitive closure of , which is to say the set of all ordered pairs of vertices in for which there exists a sequence of vertices such that the edge is in for all .〔.〕 If is acyclic, then its reachability relation is a partial order; any partial order may be defined in this way, for instance as the reachability relation of its transitive reduction.〔.〕 A noteworthy consequence of this is that since partial orders are anti-symmetric, if can reach , then we know that ''cannot'' reach . Intuitively, if we could travel from to and back to , then would contain a cycle, contradicting that it is acyclic. If is directed but ''not'' acyclic (i.e. it contains at least one cycle), then its reachability relation will correspond to a preorder instead of a partial order. 〔.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Reachability」の詳細全文を読む スポンサード リンク
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