Eur. Phys. J. B (2017) 90: 4
https://doi.org/10.1140/epjb/e2016-70415-9

Regular Article

Small-world networks on a sphere

¹ Departamento de Biofísica e Farmacologia, Centro de Biociências, Universidade Federal do Rio Grande do Norte – UFRN, 59072-970 Natal-RN, Brazil
² Escola de Engenharia e Ciências Exatas, Universidade Potiguar, 59056-450 Natal-RN, Brazil

^a e-mail: gfcorso@gmail.com

Received: 5 July 2016
Received in final form: 27 September 2016
Published online: 11 January 2017

Abstract

The Small-World Network on a Sphere SWNS is a non-crossing network that has no hubs and presents the small-world property diam ~ log N with diam being the maximal distance between any two vertices and N being the number of vertices. The SWNS is constructed using a partition of the sphere and the parallels are regular sections of the sphere with constant latitude. The number of cells on the parallels, however, increases exponentially from the pole to the equator of the sphere. We analytically compute the distribution of connectivity, the clustering coefficient and the SWNS distances. The resilience of the model against selective attacks is also discussed.