The average path length for a class of scale-free fractal hierarchical lattices: Rigorous results

Lili Pan and Xunzhi Zhu

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 3, 637-642

Abstract: With the help of the recurrence relations derived from the self-similar structure, we obtain the closed-form solution for the average path length of a class of scale-free fractal hierarchical lattices (HLs) with a general parameter q, which are simultaneously scale-free, self-similar and disassortative. Our rigorous solution shows that the average path length of the HLs grows logarithmically as d̄t∼Ntlog(2q)2 in the infinite limit of network size of Nt and that they are not small worlds but grow with a power-law relationship to the number of nodes.

Keywords: Complex networks; Hierarchical lattices; Average path length (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:3:p:637-642

DOI: 10.1016/j.physa.2009.09.051

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