The effect of zealots on the rate of consensus achievement in complex networks

In this study, we investigate the role of zealots on the result of voting process on both scale-free and Watts-Strogatz networks. We observe that inflexible individuals are very effective in consensus achievement and also in the rate of ordering process in complex networks. Zealots make the magnetization of the system to vary exponentially with time. We obtain that on SF networks, increasing the zealots' population, Z, exponentially increases the rate of consensus achievement. The time needed for the system to reach a desired magnetization, shows a power-law dependence on Z. As well, we obtain that the decay time of the order parameter shows a power-law dependence on Z. We also investigate the role of zealots' degree on the rate of ordering process and finally, we analyze the effect of network's randomness on the efficiency of zealots. Moving from a regular to a random network, the re-wiring probability Prw increases. We show that with increasing Prw, the efficiency of zealots for reducing the consensus achievement time increases. The rate of consensus is compared with the rate of ordering for different re-wiring probabilities of WS networks.