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Inside Microsoft® SQL Server™ 2005: T-SQL Querying by Dejan Sarka, Lubor Kollar, Itzik Ben-Gan

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Transitive Closure

The transitive closure of a directed graph G is the graph with the same vertices as G, and with an edge connecting each pair of nodes that are connected by a path (not necessarily containing just one edge) in G. The transitive closure helps answer a number of questions immediately, without the need to explore paths in the graph. For example, is David a manager of Aaron (directly or indirectly)? If the transitive closure of the Employees graph contains an edge from David to Aaron, he is. Does Double Espresso contain water? Can I drive from Los Angeles to New York? If the input graph contains the edges (a, b) and (b, c), there’s a transitive relationship between a and c. The transitive closure will contain the edges (a, b), (b, ...

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