In this paper, the formation control problem of the network of multiple agents is studied in terms of controllability, where the network is of the leader-follower structure with some agents taking leaders role and others being followers interconnected via the neighbor-based rule. It is shown that the controllability of a multi-agent system can be uniquely determined by the topology structure of interconnection graph. for which the investigation comes down to that for a multi-agent system with the interconnection graph being connected. Based on these observations, two kinds of uncontrollable interconnection topologies are characterized, and a necessary and sufficient eigenvector-based condition is presented. Our studies also touch upon the selection of leaders. (C) 2009 Elsevier Ltd. All rights reserved.