Figure 5: Illustration of our method to identify the set of controllable nodes.

Take as an example a simple undirected network with self-loops. (a) A step by step illustration of the diffusion process over the network from the driver node, where a control signal is applied at node 1. The newly appeared mode at each step is marked with different colors. At step 7, the iteration column vector can be expressed as a linear combination of the former modes, so the corresponding value of the control efficacy is 6. (b) For the controllability matrix , its column canonical form generated by the elementary column transformation. For a fixed value of the control efficacy measure r, the column canonical form can be performed only for r iterations of the column vector. (c) There is a one-to-one correspondence between the controllable nodes and the rows that are linearly dependent upon others in the column canonical form. In the specific case shown, there are four distinct configurations of the controllable nodes (marked in blue). Nevertheless, the number of controllable nodes is fixed and solely determined by .