Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2009-05-15
New Journal of Physics 11 (2009) 083007
Physics
Condensed Matter
Statistical Mechanics
12 pages, 7 figures. Definitive version accepted for publication in New Journal of Physics
Scientific paper
10.1088/1367-2630/11/8/083007
Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different from the model for Apollonian networks [J. S. Andrade, Jr. et al., Phys. Rev. Lett. {\bf 94}, 018702 (2005)]. We present an exhaustive analysis of various properties of our model, and obtain the analytic solutions for most of the features, including degree distribution, clustering coefficient, average path length, and degree correlations. The model recovers some striking generic characteristics observed in most real networks. To address the robustness of the relevant network properties, we compare the structural features between the investigated network and the Apollonian networks. We show that topological properties of the two networks are encoded in the way of disk packing. We argue that spatial constrains of nodes are relevant to the structure of the networks.
Chen Lichao
Ding Bailu
Guan Jihong
Zhang Zhongzhi
Zhou Shuigeng
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