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

TL;DR

This paper introduces a reaction-diffusion based model to simulate the morphogenesis of spatial networks, such as street layouts, emphasizing self-organization and local interactions.

Contribution

It presents a novel multi-layer reaction-diffusion framework for modeling the growth and evolution of spatial networks.

Findings

The model captures key features of street network development.

Metrics reveal self-organized patterns in network evolution.

Reaction-diffusion mechanisms influence network topology.

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.