تقرير
Polygon-based hierarchical planar networks based on generalized Apollonian construction
| العنوان: | Polygon-based hierarchical planar networks based on generalized Apollonian construction |
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| المؤلفون: | Tamm, M. V., Koval, D. G., Stadnichuk, V. I. |
| سنة النشر: | 2021 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics |
| الوصف: | Experimentally observed complex networks are often scale-free, small-world and have unexpectedly large number of small cycles. Apollonian network is one notable example of a model network respecting simultaneously having all three of these properties. This network is constructed by a deterministic procedure of consequentially splitting a triangle into smaller and smaller triangles. Here we present a similar construction based on consequential splitting of tetragons and other polygons with even number of edges. The suggested procedure is stochastic and results in the ensemble of planar scale-free graphs, in the limit of large number of splittings the degree distribution of the graph converges to a true power law with exponent, which is smaller than 3 in the case of tetragons, and larger than 3 for polygons with larger number of edges. We show that it is possible to stochastically mix tetragon-based and hexagon-based constructions to obtain an ensemble of graphs with tunable exponent of degree distribution. Other possible planar generalizations of the Apollonian procedure are also briefly discussed. Comment: 15 pages, 7 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2106.01321 |
| رقم الأكسشن: | edsarx.2106.01321 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |