The impact of different attack strategies on network controllability with respective to the random attack.

<p> with represents the generic dimension of controllable subspace after removing a fraction of nodes using strategy-. The nodes are removed according to six different strategies. (Strategy-0) Random attack: randomly remove fraction of nodes. (Strategy-1 or 2) Random upstream (or downstream) attack: randomly choose fraction of nodes, randomly remove one of their upstream neighbors (or downstream neighbors). The results are averaged over 10 random choices of fraction of nodes with error bars defined as s.e.m. Lines are only a guide to the eye. (Strategy-3,4, or 5) Targeted attacks: remove the top fraction of nodes according to their control centralities (or in-degrees or out-degrees).