The advent of the edge computing network paradigm places the computational and storage resources away from the data centers and closer to the edge of the network largely comprising the heterogeneous IoT devices collecting huge volumes of data. This paradigm has led to considerable improvement in network latency and bandwidth usage over the traditional cloud-centric paradigm. However, the next generation networks continue to be stymied by their inability to achieve adaptive, energy-efficient, timely data transfer in a dynamic and failure-prone environment - the very optimization challenges that are dealt with by biological networks as a consequence of millions of years of evolution. The transcriptional regulatory network (TRN) is a biological network whose innate topological robustness is a function of its underlying graph topology. In this article, we survey these properties of TRN and the metrics derived therefrom that lend themselves to the design of smart networking protocols and architectures. We then review a body of literature on bio-inspired networking solutions that leverage the stated properties of TRN. Finally, we present a vision for specific aspects of TRNs that may inspire future research directions in the fields of large-scale social and communication networks.