in this talk, we will first review the notion of pinning control, and then introduce the concept of network controllability. we will then start from the number-theoretic multiplex congruence network, showing that the nature of its controllability robustness is the inner-chain structure but not the node-degree distribution. we henceforth construct a new complex network model, referred to as the “snapback network”, and investigate its statistical properties, showing that the network robustness is not determined by the network node-degree distribution but by its inner-loop structure. we also show that the controllability robustness of the snapback network is better than random network, scale-free network and multiplex congruence network models. this investigation might shed lights onto the future study of the controllability robustness for multi-agent systems.