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

arXiv eprints
 Pub Date:
 July 2022
 DOI:
 10.48550/arXiv.2207.08527
 arXiv:
 arXiv:2207.08527
 Bibcode:
 2022arXiv220708527K
 Keywords:

 Mathematics  Probability;
 05C80;
 68W20;
 60D05;
 65D18