Flocking of the Cucker-Smale Model on General Digraphs

In the literature, the study of the Cucker-Smale (C-S) flocking model is all restricted to connected undirected graphs or digraphs of some special types, containing only a single root. In this technical note, we establish the flocking behavior of the C-S model on general digraphs, which contain all existing interaction topologies in relation to the C-S model as special cases. In particular, the topology with multiple leaders is included. The flocking results are guaranteed under some conditions on the initial state of the flock only. The critical exponent below which unconditional convergence holds is given, depending only on the interaction topology. It is consistent with the ones obtained under some known special topologies in the literature.