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This article characterizes all independence assertions that logically follow from the topology of a network and develops a linear time algorithm that identifies these assertions. The algorithm's correctness is based on the soundness of a graphical criterion, called<jats:italic>d<\/jats:italic>\u2010separation, and its optimality stems from the completeness of<jats:italic>d<\/jats:italic>\u2010separation. An enhanced version of<jats:italic>d<\/jats:italic>\u2010separation, called<jats:italic>D<\/jats:italic>\u2010separation, is defined, extending the algorithm to networks that encode functional dependencies. Finally, the algorithm is shown to work for a broad class of nonprobabilistic independencies.<\/jats:p>","DOI":"10.1002\/net.3230200504","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T09:22:04Z","timestamp":1178961724000},"page":"507-534","source":"Crossref","is-referenced-by-count":303,"title":["Identifying independence in bayesian networks"],"prefix":"10.1002","volume":"20","author":[{"given":"Dan","family":"Geiger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Verma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Judea","family":"Pearl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Mathematical Methods of Statistics","author":"Cram\u00e9r H.","year":"1964"},{"issue":"1","key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1979.tb01052.x","article-title":"Conditional independence in statistical theory","volume":"41","author":"Dawid A. 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