Shells structure in uncorrelated scale-free networks

A. Lachgar and A. Achahbar

Physica A: Statistical Mechanics and its Applications, 2019, vol. 535, issue C

Abstract: We study structure of shells in uncorrelated scale-free networks. Using probabilistic arguments, we obtain explicit expression for the distance distribution (i.e., average number of nodes at the ℓ-th shell) for different ranges of the degree exponent γ. To overcome the analytical difficulties when 2<γ<3, we show that the heterogeneous network can be approximated by a disassortative ordered network, and the average degree of neighbors of a node must depends on shells. We also deduce the mean distance between nodes, 〈ℓ〉, as the distance at which distance distribution is maximum. Taking number of nodes large, we retrieve the known scaling forms for the different ranges of γ, mainly the small-world and the ultra-small world behaviors. Very good accordance with simulations is also found. The expressions of 〈ℓ〉 involve all the network’s parameters, and can be used as good approximations of mean distance in real-world problems.

Keywords: Scale-free networks; Heterogeneous networks; Disassortative networks; Distance distribution; Mean distance (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437119313871
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:535:y:2019:i:c:s0378437119313871

DOI: 10.1016/j.physa.2019.122407

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 ().