Fast Consensus over Almost Regular Directed Graphs
Abstract
This paper studies an open consensus network design problem: identifying the optimal simple directed graphs, given a fixed number of vertices and arcs, that maximize the second smallest real part of all Laplacian eigenvalues, referred to as algebraic connectivity. For sparse and dense graphs, the class of all optimal directed graphs that maximize algebraic connectivity is theoretically identified, leading to the fastest consensus. For general graphs, a computationally efficient sequence of almost regular directed graphs is proposed to achieve fast consensus, with algebraic connectivity close to the optimal value.
Cite
@article{arxiv.2507.12726,
title = {Fast Consensus over Almost Regular Directed Graphs},
author = {Susie Lu and Marco Gamarra and Ji Liu},
journal= {arXiv preprint arXiv:2507.12726},
year = {2025}
}
Comments
This paper serves as the full version of our paper accepted to the 2025 American Control Conference and includes all complete proofs. To ensure the presentation is self-contained, some technical content overlaps with our earlier preprint arXiv:2503.23564