The herdability of structurally balanced and clustering balanced networks under the leader-follower framework is investigated. Firstly, by analyzing the network topology, a node grouping method is proposed according to the distance partition of boundary nodes. Based on this, the relationships among the topological structure, sign feature, dynamic characteristics, and controllability matrix of the structurally balanced and clustering balanced networks are analyzed, respectively, and several leader selection methods are proposed to ensure the network herdability. Furthermore, for the structurally balanced networks, a leader search algorithm with polynomial time complexity is proposed, which avoids the issue of exponential complexity increase in existing methods as the number of nodes grows, and aids in the selection of the minimum number of leaders needed to achieve the network herdability. In addition, a special clustering balanced network (star clustering balanced network) is studied, and two leader selection methods are obtained to ensure the network herdability. Finally, numerical examples are provided to illustrate the effectiveness of the theoretical results.