  In this paper, we consider a multi-agent system consisting of mobile agents
with second-order dynamics. The communication network is determined by the
so-called topological interaction rule: agents interact with a fixed number of
their closest neighbors. This rule comes from observations of real flock of
starlings. The non-symmetry of the interactions adds to the difficulty of the
analysis. The goal of this paper is to determine practical conditions (on the
initial positions and velocities of agents) ensuring that the agents
asymptotically agree on a common velocity (\ie a flocking behavior is
achieved). For this purpose, we define a notion of hierarchical structure in
the interaction graph which allows to establish such conditions, building upon
previous work on multi-agent systems with switching communication networks.
Though conservative, our approach gives conditions that can be verified a
priori. Our result is illustrated through simulations.
