Modelling complex networks by random hierarchical graphs
Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erd˝os-R´enyi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpi ´nski gasket-based gra...
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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут фізики конденсованих систем НАН України
2008
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| Schriftenreihe: | Condensed Matter Physics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/119146 |
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| Zitieren: | Modelling complex networks by random hierarchical graphs / M. Wróbel // Condensed Matter Physics. — 2008. — Т. 11, № 2(54). — С. 341-346. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-1191462017-06-05T03:03:08Z Modelling complex networks by random hierarchical graphs Wróbel, M. Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of Erd˝os-R´enyi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpi ´nski gasket-based graphs with random “decorations”. We calculate the important characteristics of these graphs – average degree, average shortest path length, small-world graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalization-group technique. Багато комплексних мереж мiстять особливi шаблони, так званi мережевi мотиви. Вони є спецiальними пiдграфами, що з’являються частiше нiж у випадкових мережах типу Ердоша-Ренi. Ми обрали один з таких шаблонiв – трикутник, i побудували сiмейство випадкових iєрархiчних графiв, визначених за гаскетом Серпiнського з випадковими “декорацiями”. Розрахованi важливi характеристики таких графiв – середнiй ступiнь, середня довжина шляху, характеристики сiмейства графiв “тiсного свiту”. Вони залежать вiд iмовiрностi декорацiй. Проаналiзовано модель Iзiнга на наших графах, описано її критичнi властивостi з використанням методу ренорм-групи. 2008 Article Modelling complex networks by random hierarchical graphs / M. Wróbel // Condensed Matter Physics. — 2008. — Т. 11, № 2(54). — С. 341-346. — Бібліогр.: 9 назв. — англ. 1607-324X PACS: 05.50.+q, 05.70.Fh, 75.10.Nr, 89.75.-k DOI:10.5488/CMP.11.2.341 http://dspace.nbuv.gov.ua/handle/123456789/119146 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 |
Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs,
which occur oftener than in randomized networks of Erd˝os-R´enyi type. We choose one of them, the triangle,
and build a family of random hierarchical graphs, being Sierpi ´nski gasket-based graphs with random “decorations”.
We calculate the important characteristics of these graphs – average degree, average shortest path
length, small-world graph family characteristics. They depend on probability of decorations. We analyze the
Ising model on our graphs and describe its critical properties using a renormalization-group technique. |
| format |
Article |
| author |
Wróbel, M. |
| spellingShingle |
Wróbel, M. Modelling complex networks by random hierarchical graphs Condensed Matter Physics |
| author_facet |
Wróbel, M. |
| author_sort |
Wróbel, M. |
| title |
Modelling complex networks by random hierarchical graphs |
| title_short |
Modelling complex networks by random hierarchical graphs |
| title_full |
Modelling complex networks by random hierarchical graphs |
| title_fullStr |
Modelling complex networks by random hierarchical graphs |
| title_full_unstemmed |
Modelling complex networks by random hierarchical graphs |
| title_sort |
modelling complex networks by random hierarchical graphs |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119146 |
| citation_txt |
Modelling complex networks by random hierarchical graphs / M. Wróbel // Condensed Matter Physics. — 2008. — Т. 11, № 2(54). — С. 341-346. — Бібліогр.: 9 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT wrobelm modellingcomplexnetworksbyrandomhierarchicalgraphs |
| first_indexed |
2025-07-08T15:19:09Z |
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2025-07-08T15:19:09Z |
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1837092516879400960 |