Data center organization and optimization are increasingly receiving attention due to the ever-growing deployments of edge and fog computing facilities. The main aim is to achieve a topology that processes the traffic flows as fast as possible and that does not only depend on AI-based computing resources, but also on the network interconnection among physical hosts. In this paper, graph theory is introduced, due to its features related to network connectivity and stability, which leads to more resilient and sustainable deployments, where cage graphs may have an advantage over the rest. In this context, the Petersen graph cage is studied as a convenient candidate for small data centers due to its small number of nodes and small network diameter, thus providing an interesting solution for edge and fog data centers.
