Random walks and diameter of finite scale-free networks

Sungmin Lee, Soon-Hyung Yook and Yup Kim

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 12, 3033-3038

Abstract: Dynamical scalings for the end-to-end distance Ree and the number of distinct visited nodes Nv of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈Ree〉 shows the dynamical scaling behavior 〈Ree(ℓ¯,t)〉=ℓ¯α(γ,N)g(t/ℓ¯z), where ℓ¯ is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, 〈Ree(ℓ¯,t)〉 in the limit t→∞ satisfies the relation 〈Ree〉∼ℓ¯α∼dα, where d is the diameter of network with d(ℓ¯)≃lnN for γ≥3 or d(ℓ¯)≃lnlnN for γ<3. Based on the scaling relation 〈Ree〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.

Keywords: Complex networks; Random walks (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437108001313
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:12:p:3033-3038

DOI: 10.1016/j.physa.2008.01.101

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().