The Complexity in Complete Graphic Characterizations of Multiagent Controllability.

Establishing the graph-based criterion for the selection of any location and any number of leaders is the main difficulty in the complete graphic characterization of multiagent controllability. This greatly increases the complexity of the study, compared with the results derived for only one or several classes of leaders. Through a detailed analysis of graphs of six nodes, this article presents a systematic design and identification process for the complete graphic characterization by taking advantage of controllability destructive nodes.