{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:37:04Z","timestamp":1787236624972,"version":"build-2736575974"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2025,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The standard definition of network efficiency assumes in an ad hoc way that network navigability occurs by shortest paths only. This is obviously not the case for the many diffusive processes occurring in real-world complex systems. Here we propose from first principles a network efficiency measure that accounts for network navigability in diffusive terms. In particular, we prove that this efficiency index is based on nonconservative (NC) diffusion processes on the network, which are ubiquitous in the real-world. We then investigate analytically several properties of this efficiency index and provide computational examples of its effectivity for the analysis of complex systems. In particular, we show that the new efficiency index of a network does not necessarily change monotonically with the removal of edges, like it trivially happens with the index based on shortest paths. It also does not change trivially with the network density, and it indeed predicts the rate of convergence to the steady state of NC diffusion.<\/jats:p>","DOI":"10.1137\/24m167038x","type":"journal-article","created":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T03:30:38Z","timestamp":1746415838000},"page":"1378-1407","source":"Crossref","is-referenced-by-count":1,"title":["Network Efficiency under Nonconservative Diffusion"],"prefix":"10.1137","volume":"24","author":[{"given":"Aitor","family":"Azemar","sequence":"first","affiliation":[{"name":"School of Mathematics & Statistics, University of Glasgow, G12 8QQ, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3066-7418","authenticated-orcid":true,"given":"Ernesto","family":"Estrada","sequence":"additional","affiliation":[{"name":"Institute for Cross-Disciplinary Physics and Complex Systems, Universitat de les Illes Balears, 07122 Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,5,6]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.brainresrev.2010.03.003"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1093\/comnet\/cnt007"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.3141\/2121-05"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.trc.2014.08.015"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2005.10.009"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulm.2004.09.006"},{"key":"ref7","volume-title":"Adaptability: The Significance of Variability from Molecule to Ecosystem","author":"Conrad M.","year":"2012"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1039\/B206169B"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2019.01.023"},{"key":"ref10","first-page":"123","author":"Deng H.","year":"2009","journal-title":"Appl. Graph Spectra"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.192407699"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.01.017"},{"key":"ref13","volume-title":"The Structure of Complex Networks: Theory and Applications","author":"Estrada E.","year":"2012"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s40324-021-00275-w"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-67802-8_21"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10699-023-09917-w"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cplett.2007.03.098"},{"key":"ref18","volume-title":"A First Course in Network Theory","author":"Estrada E.","year":"2015"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.05.032"},{"key":"ref20","unstructured":"R. Ghosh and K. Lerman, Impact of Dynamic Interactions on Multi-Scale Analysis of Community Structure in Networks, arXiv Social and Information Networks, https:\/\/api.semanticscholar.org\/CorpusID:17607159, 2012."},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0058070"},{"key":"ref22","series-title":"Math. Inst.","first-page":"155","volume-title":"Selected Topics on Applications of Graph Spectra","author":"Gutman I.","year":"2011"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/BF01164642"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.2302\/kjm.53.231"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.198701"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1017\/9781316216002"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s10618-012-0252-3"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2017.07.007"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.68.046116"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s13278-013-0134-8"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/BF01164638"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/23M1556708"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1515\/9780804766685"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroscience.2004.06.077"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1176\/appi.neuropsych.13110351"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.71.036122"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1063\/1.4953013"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M167038X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:57:22Z","timestamp":1787234242000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M167038X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,6]]},"references-count":37,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6,30]]}},"alternative-id":["10.1137\/24M167038X"],"URL":"https:\/\/doi.org\/10.1137\/24m167038x","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,6]]}}}