Condensed Matter Physics, 2008, vol. 11, No. 2(54), p. 341, English
DOI:10.5488/CMP.11.2.341
Title:
Modelling complex networks by random hierarchical graphs
Author(s):

M.Wróbel
(Institute of Mathematics, Maria CurieSkłodowska University, Lublin, Poland)

Numerous complex networks contain special patterns, called network motifs. These are specific subgraphs, which occur oftener than in randomized networks of ErdősRényi type. We choose one of them, the triangle, and build a family of random hierarchical graphs, being Sierpiński gasketbased graphs with random "decorations". We calculate the important characteristics of these graphs  average degree, average shortest path length, smallworld graph family characteristics. They depend on probability of decorations. We analyze the Ising model on our graphs and describe its critical properties using a renormalizationgroup technique.
Key words:
random graphs, Ising model, complex networks, network motifs
PACS:
05.50.+q, 05.70.Fh, 75.10.Nr, 89.75.k
