✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.