{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:48:13Z","timestamp":1753876093258,"version":"3.41.2"},"reference-count":51,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2019,8,2]],"date-time":"2019-08-02T00:00:00Z","timestamp":1564704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"ICP RAS","award":["0082-2014-0001","AAAA-A17-117040610310-6"],"award-info":[{"award-number":["0082-2014-0001","AAAA-A17-117040610310-6"]}]},{"DOI":"10.13039\/501100002261","name":"RFBR","doi-asserted-by":"publisher","award":["18-29-13013"],"award-info":[{"award-number":["18-29-13013"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100015695","name":"Basis Foundation","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100015695","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100002261","name":"RFBR","doi-asserted-by":"publisher","award":["19-02-00214"],"award-info":[{"award-number":["19-02-00214"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic Research Program"},{"DOI":"10.13039\/501100007251","name":"National Research University Higher School of Economics","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007251","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider clustering in rewired Erd\u0151s\u2013R\u00e9nyi networks with conserved vertex degree and in random regular graphs from the localization perspective. It has been found in Avetisov et al. (2016, Phys. Rev. E, 94, 062313) that at some critical value of chemical potential $\\mu_{\\rm cr}$ of closed triad of bonds, the evolving networks decay into the maximally possible number of dense subgraphs. The adjacency matrix acquires above $\\mu_{\\rm cr}$ the two-zonal support with the triangle-shaped main (perturbative) zone separated by a wide gap from the side (non-perturbative) zone. Studying the distribution of gaps between neighbouring eigenvalues (the level spacing), we demonstrate that in the main zone the level spacing matches the Wigner\u2013Dyson law and is delocalized, however it shares the Poisson statistics in the side zone, which is the signature of localization. In parallel with the evolutionary designed networks, we consider \u2018instantly\u2019 ad hoc prepared networks with in- and cross-cluster probabilities exactly as at the final stage of the evolutionary designed network. For such \u2018instant\u2019 networks the eigenvalues are delocalized in both zones. We speculate about the difference in eigenvalue statistics between \u2018evolutionary\u2019 and \u2018instant\u2019 networks from the perspective of a possible phase transition between ergodic and non-ergodic network patterns with a strong \u2018memory dependence\u2019, thus advocating possible existence of non-ergodic delocalized states in the clustered random networks at least at finite network sizes.<\/jats:p>","DOI":"10.1093\/comnet\/cnz026","type":"journal-article","created":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T11:25:41Z","timestamp":1563967541000},"source":"Crossref","is-referenced-by-count":17,"title":["Localization and non-ergodicity in clustered random networks"],"prefix":"10.1093","volume":"8","author":[{"given":"V","family":"Avetisov","sequence":"first","affiliation":[{"name":"N.N. Semenov Institute of Chemical Physics RAS, Moscow, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A","family":"Gorsky","sequence":"additional","affiliation":[{"name":"Institute for Information Transmission Problems RAS, Moscow, Russian Federation and Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S","family":"Nechaev","sequence":"additional","affiliation":[{"name":"Interdisciplinary Scientific Center Poncelet (CNRS UMI 2615), Moscow, Russian Federation and Lebedev Physical Institute RAS, Moscow, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O","family":"Valba","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Research University Higher School of Economics, Moscow, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2019,8,2]]},"reference":[{"key":"2020072910570261600_B1","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0378-4371(02)01181-0","article-title":"Networks in life: scaling properties and eigenvalue spectra.","volume":"314","author":"Farkasa","year":"2002","journal-title":"Physica A"},{"key":"2020072910570261600_B2","doi-asserted-by":"crossref","first-page":"026704","DOI":"10.1103\/PhysRevE.64.026704","article-title":"Spectra of real-world graphs: beyond the semicircle law.","volume":"64","author":"Farkasa","year":"2001","journal-title":"Phys. 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