Impact of boundaries on fully connected random geometric networks

TL;DR

This paper investigates how boundary effects influence the transition to full connectivity in random geometric networks, revealing boundary-dependent phenomena and offering insights for network design across various geometries.

Contribution

It introduces a method to distinguish connectivity properties considering boundary effects, highlighting the impact of domain boundaries on network connectivity transitions.

Findings

Boundary effects significantly influence full connectivity transitions.

A new approach distinguishes bulk from boundary contributions.

The method aids in designing networks with desired connectivity properties.

Abstract

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.