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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| Опубліковано в: : | Condensed Matter Physics |
|---|---|
| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709482293821440 |
|---|---|
| author | Kotorowicz, Monika Kozitsky, Yuri |
| author_facet | Kotorowicz, Monika Kozitsky, Yuri |
| 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. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| 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.
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.
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| first_indexed | 2025-12-07T17:18:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-119972 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T17:18:00Z |
| publishDate | 2011 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Kotorowicz, Monika Kozitsky, Yuri 2017-06-10T14:06:39Z 2017-06-10T14:06:39Z 2011 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 https://nasplib.isofts.kiev.ua/handle/123456789/119972 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. The authors benefited from fruitful discussions on the matter of this work held with our colleagues Yuri Kondratiev and Vasyl Ustimenko for which they are cordially grateful. The authors are also grateful to the unnamed referee whose remarks and suggestions were helpful in improving the presentation of the article. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Motif based hierarchical random graphs: structural properties and critical points of an Ising model Iєрархiчнi випадковi графи з мотивiв:структурнi властивостi та критичнi точки моделi Iзiнга Article published earlier |
| spellingShingle | Motif based hierarchical random graphs: structural properties and critical points of an Ising model Kotorowicz, Monika Kozitsky, Yuri |
| title | Motif based hierarchical random graphs: structural properties and critical points of an Ising model |
| title_alt | Iєрархiчнi випадковi графи з мотивiв:структурнi властивостi та критичнi точки моделi Iзiнга |
| 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119972 |
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