Fig. 1

Targeted structural controlability. The targeted structural controllability problem for the directed graph G=(V,E) with n nodes and a subset T⊆V with I target nodes, is equivalent with deciding if there exists a set of l directed paths in G such that each node in T is an end point of one such path and no two paths intersect at the same distance from their end points, [15]. In this example, the paths from the driven nodes D₁, D₂ to the target nodes T₁−T₄ intersect in the internal nodes A, B, and C. The controllability theorem of [15] implies that the lengths of the paths CT₂ and CT₃ is different, and that either the length of the path AT₁, AT₂, and AT₃ are pairwise different, or the length of the path B_T2, B_T3, and BT₄ are pair-wise different (or both)