Sequential construction of spatial networks with arbitrary degree sequence and edge length distribution

TL;DR

This paper introduces a numerical method for constructing spatial networks with specified degree and edge length distributions, enabling unbiased sampling of complex geometric graphs relevant to various physical and communication systems.

Contribution

The authors develop a novel numerical approach for generating spatial networks with arbitrary degree and edge length distributions, improving sampling accuracy and applicability.

Findings

Method accurately reproduces target distributions asymptotically

Small errors in distribution matching are observed in some cases

A positive fraction of networks can be constructed in boundary scenarios

Abstract

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they inherit their properties from the embedding space as well as from the constraints imposed on the network's structure by design, for example, the degree sequence. Here we consider geometric graphs with a given distribution for vertex degrees and edge lengths and propose a numerical method for unbiased sampling of such graphs. We show that the method reproduces the desired target distributions up to a small error asymptotically, and that is some boundary cases only a positive fraction of the network is guaranteed to possible to construct.