Hierarchy is an efficient way for a group to organize, but often goes along with inequality that benefits leaders. To control despotic behaviour, followers can assess leaders’ decisions by aggregating their own and their neighbours’ experience, and in response challenge despotic leaders. But in hierarchical social networks, this interactional justice can be limited by (i) the high influence of a small clique who are treated better, and (ii) the low connectedness of followers. Here we study how the connectedness of a social network affects the co-evolution of despotism in leaders and tolerance to despotism in followers. We simulate the evolution of a population of agents, where the influence of an agent is its number of social links. Whether a leader remains in power is controlled by the overall satisfaction of group members, as determined by their joint assessment of the leaders behaviour. We demonstrate that centralization of a social network around a highly influential clique greatly increases the level of despotism. This is because the clique is more satisfied, and their higher influence spreads their positive opinion of the leader throughout the network. Finally, our results suggest that increasing the connectedness of followers limits despotism while maintaining hierarchy.