Small-world networks on a sphere

The Small-World Network on a Sphere SWNS is a non-crossing network that has no hubs and presents the small-world property diam similar to logN 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.