At the verge of the launch of the first commercial fifth generation (5G) system, trends in wireless and optical networks are proceeding toward increasingly dense deployments, supporting resilient interconnection for applications that carry higher and higher capacity and tighter latency requirements. These developments put increasing pressure on network backhaul and drive the need for a re-examination of traditional backhaul topologies. Challenges of impending networks cannot be tackled by star and ring approaches due to their lack of intrinsic survivability and resilience properties, respectively. In support of this re-examination, we propose a backhaul topology design method that formulates the topology optimization as a graph optimization problem by capturing both the objective and constraints of optimization in graph invariants. Our graph theoretic approach leverages well studied mathematical techniques to provide a more systematic alternative to traditional approaches to backhaul design. Specifically, herein, we optimize over some known graph invariants, such as maximum node degree, topology diameter, average distance, and edge betweenness, as well as over a new invariant called node Wiener impact, to achieve baseline backhaul topologies that match the needs for resilient future wireless and optical networks.