Decentralized formation of random regular graphs for robust multi-agent networks

Abstract

Abstract-Multi-agent networks are often modeled via interaction graphs, where the nodes represent the agents and the edges denote direct interactions between the corresponding agents. Interaction graphs have significant impact on the robustness of networked systems. One family of robust graphs is the random regular graphs. In this paper, we present a locally applicable reconfiguration scheme to build random regular graphs through self-organization. For any connected initial graph, the proposed scheme maintains connectivity and the average degree while minimizing the degree differences and randomizing the links. As such, if the average degree of the initial graph is an integer, then connected regular graphs are realized uniformly at random as time goes to infinity.

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

“…Note that if k ∈ N, then G 0 n,k = ∅. A thorough analysis of the dynamics induced by Algorithm I along with the following result can be found in [19]. Theorem 4.2 Let G n,k satisfy k ∈ N. Then, P RR has a unique limiting distribution, µ * , satisfying…”

“…A thorough analysis of the dynamics induced by Algorithm I along with the following result can be found in [19].…”

“…In this paper, we present a decentralized scheme to transform any connected interaction graph into a connected random regular graph with a similar number of edges as the initial graph. Some preliminary results of this work were presented in [18] and [19], where any initial graph with an integer average degree, k ∈ N, was transformed into a random k-regular graph. In this paper, we extend our earlier works to obtain a method that is applicable to the most generic case, i.e.…”