{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T20:10:30Z","timestamp":1697746230964},"reference-count":2,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8625,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1983,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>D = (V, A<\/jats:italic>) be a weighted digraph with vertex set <jats:italic>V<\/jats:italic> and arc set <jats:italic>A<\/jats:italic>, and let \u03b1 be a one\u2010to\u2010one mapping from <jats:italic>V<\/jats:italic> onto the set of integers {1, 2, \u2026, |<jats:italic>V<\/jats:italic>|}. A mapping \u03b1 is called a ranking of <jats:italic>D<\/jats:italic>. According to a ranking \u03b1, the arc set <jats:italic>A<\/jats:italic> is naturally partitioned into the set of forward arcs of \u03b1 and that of backward ones. By using these subsets of rankings, we define three kinds of optimal rankings: forward optimal rankings, backward optimal rankings, and mutual optimal rankings. Since many results on the backward optimal rankings are already known, we mainly discuss the properties of the forward optimal rankings and the mutual ones in the present article.<\/jats:p>","DOI":"10.1002\/net.3230130109","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T15:00:40Z","timestamp":1178895640000},"page":"143-151","source":"Crossref","is-referenced-by-count":6,"title":["Ranking the vertices of a weighted digraph using the length of forward arcs"],"prefix":"10.1002","volume":"13","author":[{"given":"Mikio","family":"Kano","sequence":"first","affiliation":[]},{"given":"Akio","family":"Sakamoto","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"M.KanoandA.Sakamoto Ranking the vertices of a paired comparison digraph. Unpublished."},{"key":"e_1_2_1_3_2","unstructured":"M.KanoandA.Sakamoto Ranking the vertices of a paired comparison digraph. II. Normal completeness theorems. Unpublished."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230130109","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230130109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T19:57:21Z","timestamp":1697745441000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230130109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,3]]},"references-count":2,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1983,3]]}},"alternative-id":["10.1002\/net.3230130109"],"URL":"https:\/\/doi.org\/10.1002\/net.3230130109","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,3]]}}}