Spatial networks evolving to reduce length

Motivated by results of Henry et al. (2011, PNAS, 108, 8605-8610), we propose a general scheme for evolving spatial networks to reduce their total edge lengths. We study the properties of the equilibria of two networks from this class, which interpolate between three well-studied objects: the Erdós-Rényi random graph, the random geometric graph and the minimum spanning tree. The first of our two evolutions can be used as a model for a social network where individuals have fixed opinions about a number of issues and adjust their ties to be connected to people with similar views. The second evolution which preserves the connectivity of the network has potential applications in the design of transportation networks and other distribution systems.

Duke Scholars

Author Richard Timothy Durrett Mathematics