Morphogenesis of complex networks: a reaction diffusion framework for spatial graphs

Abstract

A large variety of real systems are composed by entities in relationships which can be represented by networks. In many of these systems, elements are embedded in the space and location information impacts properties and evolution. Local interactions between elements generate different kinds of equilibrium and often indicate a self-organized behaviour. In this paper we are interested in essential mechanisms behind morphogenesis of spatial networks such as street networks. We propose a multi-layer model, where a reaction-diffusion mechanism governs the growth of spatial networks. We study its evolution with some metrics.