Forecasting of multivariate time-series is an important problem that has applications in traffic management, cellular network configuration, and quantitative finance. A special case of the problem arises when there is a graph available that captures the relationships between the time-series. In this paper we propose a novel learning architecture that achieves performance competitive with or better than the best existing algorithms, without requiring knowledge of the graph. The key element of our proposed architecture is the learnable fully connected hard graph gating mechanism that enables the use of the state-of-the-art and highly computationally efficient fully connected time-series forecasting architecture in traffic forecasting applications. Experimental results for two public traffic network datasets illustrate the value of our approach, and ablation studies confirm the importance of each element of the architecture. The code is available here: https://github.com/boreshkinai/fc-gaga.