Toward Stronger Robustness of Network Controllability: A Snapback Network Model

A new complex network model, called <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -snapback network, is introduced. Basic topological characteristics of the network, such as degree distribution, average path length, clustering coefficient, and Pearson correlation coefficient, are evaluated. The typical 4-motifs of the network are simulated. The robustness of both state and structural controllabilities of the network against targeted and random node- and edge-removal attacks, with comparisons to the multiplex congruence network and the generic scale-free network, are presented. It is shown that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -snapback network has the strongest robustness of controllabilities due to its advantageous inherent structure with many chain and loop motifs.