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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| Date: | 2008 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2008
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| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/119146 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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