Given a social network, can we quickly 'zoom-out' of the graph? Is there a smaller equivalent representation of the graph that preserves its propagation characteristics? Can we group nodes together based on their influence properties? These are important problems with applications to influence analysis, epidemiology and viral marketing applications. In this paper, we first formulate a novel Graph Coarsening Problem to find a succinct representation of any graph while preserving key characteristics for diffusion processes on that graph. We then provide a fast and effective near-linear-time (in nodes and edges) algorithm COARSENET for the same. Using extensive experiments on multiple real datasets, we demonstrate the quality and scalability of COARSENET, enabling us to reduce the graph by 90% in some cases without much loss of information. Finally we also show how our method can help in diverse applications like influence maximization and detecting patterns of propagation at the level of automatically created groups on real cascade data.