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

✍ Scribed by Lili Pan; Xunzhi Zhu


Book ID
103884305
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
456 KB
Volume
389
Category
Article
ISSN
0378-4371

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✦ Synopsis


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 dt ∼ N log(2q) 2 t in the infinite limit of network size of N t and that they are not small worlds but grow with a power-law relationship to the number of nodes.