The polymer brush normally swells in a good solvent, while it collapses in a poor solvent. An abnormal response of polymer brush, so-called co-nonsolvency, is a phenomenon where the brush collapses counter-intuitively in a good solvent mixture. In this work, the structural properties of the co-nonsolvency in the grafted polymers are investigated using molecular dynamics simulation. We consider the brushes at three different grafting densities to study the effect of topologically excluded volumes on the co-nonsolvency. Preferential adsorption of solvent molecules on the polymers leads to the formation of a bridging structure between them, which causes the polymer brush to collapse significantly. We find that the intermolecular bridging structure is predominant in the overlapping brush regime, while the intramolecular bridging is only formed in the mushroom brush regime. Topological constraints also affect the degree of collapse as well as the orientation of the polymer substantially. Based on these observations, we construct a phase diagram of the polymer brush system using the average thickness and orientation as structural order parameters when both the grafting density and the fraction of the solvent mixture are varied, respectively. Going beyond previous works 1 arXiv:1905.13478v1 [cond-mat.soft] 31 May 2019 on the co-nonsolvency in the single polymer model and adsorption-attraction model, this work provides a microscopic insight into many-chain effects on the co-nonsolvency behavior in a systematic way. Furthermore, the phase diagrams presented in this work can provide useful theoretical guidelines for controlling co-nonsolvency behavior in various polymer brush systems such as bio-interface, drug-delivery, and sensor devices.