Control of the global parameters of complex networks has been explored experimentally in a variety of contexts. Yet, the more difficult prospect of realizing arbitrary network architectures, especially analog physical networks, that provide dynamical control of individual nodes and edges has remained elusive. It also proves challenging to measure a complex networks full internal dynamics given the vast hierarchy of timescales involved. These span from the fastest nodal dynamics to very slow epochs over which emergent global phenomena, including network synchronization and the manifestation of exotic steady states, eventually emerge. In this effort we have realized and demonstrated an experimental system satisfying these requirements. It is based upon modular, fully controllable, nonlinear radio-frequency nanomechanical oscillators, designed to form the nodes of complex dynamical networks with edges configured with arbitrary topology. The dynamics of these oscillators and their surrounding network are analog, continuous-valued and can be fully interrogated in real time. Our embodiment permits network interconnections solely in the electrical domain, and provides unprecedented node and edge control over a vast region in parameter space. Continuous measurement of the instantaneous amplitudes and phases of every constituent oscillator node are enabled, yielding full and detailed network data without reliance upon statistical quantities.