A Simulation Study of Consensus Speed over Scale-Free Networks

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 (dmin) for the nodes, the algebraic connectivity (λ2) of the network topology is studied, as well as the time (tc) (or iteration (kc), for discrete algorithm) taken to reach consensus. The results exhibit that λ2 decreases while γ increases. The λ2 increases monotonically as dmin grows, and they fit very well in a linear relationship. tc (or kc) decreases as γ reduces and dmin increases. Via observing the behavior of the largest eigenvalue (λn) 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.