The graph augmentation problem seeks to suggest new edges that, when added to an input graph, improve the overall connectivity of the nodes. For social network applications, the latter is typically computed as the average shortest path length in the network. In this work we first introduce one interesting variation of the problem that focuses on improving the connectivity between nodes belonging to a specific sub-graph (for instance nodes of the same class or users that share interests). Key to our method for solving the original graph augmentation problem and its suggested variation is an intuitive algorithm we propose. The algorithm operates by first constructing a summary graph that retains important structural properties of the input graph. Using this summary our algorithm computes an effective list of suggested shortcuts. Unlike existing techniques, the proposed algorithm does not require complex computations over the whole graph (such as the computation of all-pair shortest paths). This makes it applicable for larger graphs where existing proposals fail to operate. Our experimental results demonstrate the efficiency and effectiveness of our techniques on graphs of various sizes and characteristics.