Herdability of signed networks based on leader role

The paper investigates the herdability of signed networks from the perspective of leader role. First, we analyze the influence of interactions between leaders on the herdability of networks, which shows that the interactions between leaders do not influence the herdability of networks. Furthermore, we propose a necessary and sufficient condition for the herdability of the leader-composite networks, which indicates that the leader-composite network is herdable if and only if all disjoint subnetworks are herdable. In addition, we focus on the herdability of cycle networks, and give some leader selection methods to realize the herdability of cycle networks. The illustrative examples are provided to demonstrate the validity of the theoretical results.