A Simulation Study of Consensus Speed over Scale-Free Networks

Abstract Scale-free network and consensus among multiple agents have both drawn quite much attention. To investigate the consensus speed over scale-free networks is the main topic in this paper. Given a set of different values for the power-law distribution parameter γ, and a set of different values for the minimum degree ( d min ) for the nodes, the algebraic connectivity (λ 2 ) of the network topology is studied, as well as the time ( t c ) (or iteration ( k c ), for discrete algorithm) taken to reach consensus. The results exhibit that λ 2 decreases while γ increases. The λ 2 increases monotonically as d min grows, and they fit very well in a linear relationship. t c (or k c ) decreases as γ reduces and d min increases. Via observing the behavior of the largest eigenvalue (λ n ) of the Laplacian of the network topology, we draw the conclusion that the robustness over time delays declines while the robustness over node-failures and edge-failures increases.