Motif based hierarchical random graphs: structural properties and critical points of an Ising model
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824 – 827]. The construction scheme resembles that used in [Hinczewsk...
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2011
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119972 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Motif based hierarchical random graphs: structural properties and critical points of an Ising model / Monika Kotorowicz, Yuri Kozitsky // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13801: 1-18. — Бібліогр.: 30 назв. — англ. |
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irk-123456789-1199722017-06-11T03:04:03Z Motif based hierarchical random graphs: structural properties and critical points of an Ising model Kotorowicz, Monika Kozitsky, Yuri A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824 – 827]. The construction scheme resembles that used in [Hinczewski M., A. Nihat Berker, Phys. Rev. E, 2006, 73, 066126], according to which the short-range bonds are non-random, whereas the long-range bonds appear independently with the same probability. A number of structural properties of the graphs have been described, among which there are degree distributions, clustering, amenability, small-world property. For one of the motifs, the critical point of the Ising model defined on the corresponding graph has been studied. Вводиться i вивчається клас випадкових графiв, збудованих в алгоритмiчний спосiб з п’яти мотивiв, знайдених у [Milo R., Shen-Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824]. Конструкцiйна схема нагадує схему, застосовану у [Hinczewski M., A. Nihat Berker, Phys. Rev. E, 2006, 73, 066126], згiдно з якою короткосяжнi ребра є невипадковi, тодi як довгосяжнi ребра виникають незалежно iз однаковою ймовiрнiстю. Описано ряд структурних властивостей графiв, серед яких є розподiл ступенiв, кластернiсть, аменабiльнiсть, властивiсть тiсного свiту. Для одного з мотивiв вивчається критична точка моделi Iзiнга, визначеної на вiдповiдному графi. 2011 Article Motif based hierarchical random graphs: structural properties and critical points of an Ising model / Monika Kotorowicz, Yuri Kozitsky // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13801: 1-18. — Бібліогр.: 30 назв. — англ. 1607-324X PACS: 89.75.Fb, 89.75.Kd, 05.10.Cc, 05.70.Jk DOI:10.5488/CMP.14.13801 arXiv:1106.4399 http://dspace.nbuv.gov.ua/handle/123456789/119972 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A class of random graphs is introduced and studied. The graphs are constructed in an algorithmic way from five motifs which were found in [Milo R., Shen Orr S., Itzkovitz S., Kashtan N., Chklovskii D., Alon U., Science, 2002, 298, 824 – 827]. The construction scheme resembles that used in [Hinczewski M., A. Nihat Berker, Phys. Rev. E, 2006, 73, 066126], according to which the short-range bonds are non-random, whereas the long-range bonds appear independently with the same probability. A number of structural properties of the graphs have been described, among which there are degree distributions, clustering, amenability, small-world property. For one of the motifs, the critical point of the Ising model defined on the corresponding graph has been studied. |
| format |
Article |
| author |
Kotorowicz, Monika Kozitsky, Yuri |
| spellingShingle |
Kotorowicz, Monika Kozitsky, Yuri Motif based hierarchical random graphs: structural properties and critical points of an Ising model Condensed Matter Physics |
| author_facet |
Kotorowicz, Monika Kozitsky, Yuri |
| author_sort |
Kotorowicz, Monika |
| title |
Motif based hierarchical random graphs: structural properties and critical points of an Ising model |
| title_short |
Motif based hierarchical random graphs: structural properties and critical points of an Ising model |
| title_full |
Motif based hierarchical random graphs: structural properties and critical points of an Ising model |
| title_fullStr |
Motif based hierarchical random graphs: structural properties and critical points of an Ising model |
| title_full_unstemmed |
Motif based hierarchical random graphs: structural properties and critical points of an Ising model |
| title_sort |
motif based hierarchical random graphs: structural properties and critical points of an ising model |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119972 |
| citation_txt |
Motif based hierarchical random graphs: structural
properties and critical points of an Ising model
/ Monika Kotorowicz, Yuri Kozitsky // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13801: 1-18. — Бібліогр.: 30 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT kotorowiczmonika motifbasedhierarchicalrandomgraphsstructuralpropertiesandcriticalpointsofanisingmodel AT kozitskyyuri motifbasedhierarchicalrandomgraphsstructuralpropertiesandcriticalpointsofanisingmodel |
| first_indexed |
2023-10-18T20:35:52Z |
| last_indexed |
2023-10-18T20:35:52Z |
| _version_ |
1796150617230540800 |