{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T23:09:32Z","timestamp":1770332972149,"version":"3.49.0"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100006733","name":"CHED","doi-asserted-by":"crossref","award":["PHERNET"],"award-info":[{"award-number":["PHERNET"]}],"id":[{"id":"10.13039\/501100006733","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p>Ideal flow network is a strongly connected network with flow, where the flows are in steady state and conserved. The matrix of ideal flow is premagic, where vector, the sum of rows, is equal to the transposed vector containing the sum of columns. The premagic property guarantees the flow conservation in all nodes. The scaling factor as the sum of node probabilities of all nodes is equal to the total flow of an ideal flow network. The same scaling factor can also be applied to create the identical ideal flow network, which has from the same transition probability matrix. Perturbation analysis of the elements of the stationary node probability vector shows an insight that the limiting distribution or the stationary distribution is also the flow-equilibrium distribution. The process is reversible that the Markov probability matrix can be obtained from the invariant state distribution through linear algebra of ideal flow matrix. Finally, we show that recursive transformation [Formula: see text] to represent [Formula: see text]-vertices path-tracing also preserved the properties of ideal flow, which is irreducible and premagic.<\/jats:p>","DOI":"10.1142\/s1793830918500738","type":"journal-article","created":{"date-parts":[[2018,9,3]],"date-time":"2018-09-03T06:40:38Z","timestamp":1535956838000},"page":"1850073","source":"Crossref","is-referenced-by-count":1,"title":["Ideal flow of Markov Chain"],"prefix":"10.1142","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1123-5924","authenticated-orcid":false,"given":"Kardi","family":"Teknomo","sequence":"first","affiliation":[{"name":"Ateneo Pedestrian and Traffic Computing Laboratory, Department of Information Systems &amp; Computer Science, Ateneo de Manila University, Philippines"}]}],"member":"219","published-online":{"date-parts":[[2018,12,26]]},"reference":[{"key":"S1793830918500738BIB001","volume-title":"Iterative Solution Methods","author":"Axelsson O.","year":"1996"},{"key":"S1793830918500738BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-19592-1"},{"key":"S1793830918500738BIB004","doi-asserted-by":"crossref","DOI":"10.1201\/9781482296426","volume-title":"Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference","author":"Gamerman D.","year":"2006","edition":"2"},{"key":"S1793830918500738BIB005","volume-title":"Nonnegative Matrices and Applicable Topics in Linear Algebra","author":"Graham A.","year":"1987"},{"key":"S1793830918500738BIB006","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/57.1.97"},{"key":"S1793830918500738BIB008","volume-title":"Magic Squares and Cubes Paperback","author":"Mack W. S.","year":"2012"},{"key":"S1793830918500738BIB009","volume-title":"Fundamentals of Electric Circuits: Concepts and Analysis","author":"Mathew A.","year":"2012"},{"key":"S1793830918500738BIB010","volume-title":"Markov Chains","author":"Norris J.","year":"1998"},{"key":"S1793830918500738BIB011","volume-title":"Non-negative Matrices and Markov Chains","author":"Seneta E.","year":"2013"},{"key":"S1793830918500738BIB012","doi-asserted-by":"publisher","DOI":"10.1201\/b10589"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830918500738","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,8]],"date-time":"2020-11-08T18:41:39Z","timestamp":1604860899000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830918500738"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12]]},"references-count":10,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2018,12,26]]},"published-print":{"date-parts":[[2018,12]]}},"alternative-id":["10.1142\/S1793830918500738"],"URL":"https:\/\/doi.org\/10.1142\/s1793830918500738","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12]]}}}