{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T09:32:05Z","timestamp":1762075925707},"reference-count":22,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":9902,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1979,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A network N considered here is a graph (G,E) whose edge e is weighted by I(e) = [\u03b1(e), \u03b2(e)]. An admissible flow is a flow f satisfying \u03b1(e) \u2286 f (e) \u2286 \u03b2(e), for all e \u2282 E. A necessary and sufficient condition for existence of admissible Boolean flows in N, and characterization of maximum Boolean flows are presented. Then a property of maximum Boolean flows which are the terminal capacities of two\u2010terminal Boolean flows satisfy a Boolean triangular inequality is shown. Finally the concept of \u03b3\u2010relativeness of a symmetric Boolean mapping m for any threshould \u03b3\u2286 S which induces a cluster decomposition of the node set V, by introducing Boolean network metrics is presented.<\/jats:p>","DOI":"10.1002\/net.3230090305","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T10:25:52Z","timestamp":1178879152000},"page":"249-281","source":"Crossref","is-referenced-by-count":4,"title":["A boolean theory of network flows and metrics and its applications to particle transmission and clustering"],"prefix":"10.1002","volume":"9","author":[{"given":"K.","family":"Onaga","sequence":"first","affiliation":[]},{"given":"W.","family":"Mayeda","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"issue":"2","key":"e_1_2_1_2_2","first-page":"92","article-title":"Properties of Boolean flows in networks","volume":"59","author":"Onage K.","year":"1976","journal-title":"Trans. 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