The paper studies the controllability problem for multi-agent systems with leader-follower structure. The
relationship between system controllability and communication topology is characterized based on graph theory. A graph
theoretic criterion for controllability is provided. The concept of symmetry is extended to multi-leaders systems through
permutation group theory, it is proved that both topology symmetry and equitable partition are two special cases of relaxed
equitable partitions. Simulation results show effectiveness of proposed method.