Effect of edge pruning on structural controllability and observability of complex networks

Controllability and observability of complex systems are vital concepts in many fields of science. The network structure of the system plays a crucial role in determining its controllability and observability. Because most naturally occurring complex systems show dynamic changes in their network connectivity, it is important to understand how perturbations in the connectivity affect the controllability of the system. To this end, we studied the control structure of different types of artificial, social and biological neuronal networks (BNN) as their connections were progressively pruned using four different pruning strategies. We show that the BNNs are more similar to scale-free networks than to small-world networks, when comparing the robustness of their control structure to structural perturbations. We introduce a new graph descriptor, 'the cardinality curve', to quantify the robustness of the control structure of a network to progressive edge pruning. Knowing the susceptibility of control structures to different pruning methods could help design strategies to destroy the control structures of dangerous networks such as epidemic networks. On the other hand, it could help make useful networks more resistant to edge attacks.