On graph theoretic results underlying the analysis of consensus in multi-agent systems

TL;DR

This paper corrects significant errors and inaccuracies in a foundational work on consensus in multi-agent systems, providing stronger results and clarifying the interpretation of priority within the context.

Contribution

It offers corrections to a key paper on multi-agent consensus, introduces stronger theoretical results, and clarifies the concept of priority in the analysis.

Findings

Corrected a serious mistake in the original paper

Presented stronger results for consensus analysis

Clarified the interpretation of priority

Abstract

This note corrects a pretty serious mistake and some inaccuracies in "Consensus and cooperation in networked multi-agent systems" by R. Olfati-Saber, J.A. Fax, and R.M. Murray, published in Vol. 95 of the Proceedings of the IEEE (2007, No. 1, P. 215-233). It also mentions several stronger results applicable to the class of problems under consideration and addresses the issue of priority whose interpretation in the above-mentioned paper is not exact.