The development of disease involves a systematic disturbance inside cells and is associated with changes in the interactions or regulations among genes forming biological networks. The bridges inside a network are critical in shortening the distances between nodes. We observed that, inside the human gene regulatory network, one strongly connected core bridged the whole network. Other regulations outside the core formed a weakly connected component surrounding the core like a peripheral structure. Furthermore, the regulatory feedback loops (FBLs) inside the core compose an interface-like structure between the core and periphery. We then denoted the regulatory FBLs as the interface core. Notably, both the cancer-associated and essential biomolecules and regulations were significantly overrepresented in the interface core. These results implied that the interface core is not only critical for the network structure but central in cellular systems. Furthermore, the enrichment of the cancer-associated and essential regulations in the interface core might be attributed to its bridgeness in the network. More importantly, we identified one regulatory FBL between HNF4A and NR2F2 that possesses the highest bridgeness in the interface core. Further investigation suggested that the disturbance of the HNF4A-NR2F2 FBL might protect tumor cells from apoptotic processes. Our results emphasize the relevance of the regulatory network properties to cellular systems and might reveal a critical role of the interface core in cancer.