Formation of Robust Multi-Agent Networks Through Self-Organizing Random Regular Graphs

TL;DR

This paper introduces a decentralized method for transforming any connected multi-agent network into a robust, well-connected random regular graph, enhancing network resilience with minimal sparsity change.

Contribution

It proposes a novel decentralized scheme to convert arbitrary connected graphs into random regular graphs, improving robustness while maintaining sparsity.

Findings

Transforms any connected graph into a random regular graph.

Enhances network robustness against failures and attacks.

Maintains network sparsity with minimal modifications.

Abstract

Multi-agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m in [k, k + 2]. Accordingly, the agents improve the robustness of the network with a minimal change in the overall sparsity by optimizing the graph connectivity through the proposed local operations.