Motif based hierarchical random graphs: structural properties and critical points of an Ising model

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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Veröffentlicht in:Condensed Matter Physics
Datum:2011
Hauptverfasser: Kotorowicz, Monika, Kozitsky, Yuri
Format: Artikel
Sprache:English
Veröffentlicht: Інститут фізики конденсованих систем НАН України 2011
Online Zugang: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
Zitieren: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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-119972
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Motif based hierarchical random graphs: structural properties and critical points of an Ising model
spellingShingle Motif based hierarchical random graphs: structural properties and critical points of an Ising model
Kotorowicz, Monika
Kozitsky, Yuri
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
author Kotorowicz, Monika
Kozitsky, Yuri
author_facet Kotorowicz, Monika
Kozitsky, Yuri
publishDate 2011
language English
container_title Condensed Matter Physics
publisher Інститут фізики конденсованих систем НАН України
format Article
title_alt Iєрархiчнi випадковi графи з мотивiв:структурнi властивостi та критичнi точки моделi Iзiнга
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.
issn 1607-324X
url https://nasplib.isofts.kiev.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.
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first_indexed 2025-12-07T17:18:00Z
last_indexed 2025-12-07T17:18:00Z
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