We introduce a new graph sparsification method that targets the neighborhood information available for each node. Our approach is motivated by the fact that neighborhood information is used by several mining and learning tasks on graphs as well as reachability queries. The result of our sparsification technique is a sparsified graph that can be used instead of the original graph in the above tasks while still ensuring fairly good approximations for the results. Moreover, our sparsification method allows users to control the size of the resulting sparsified graph by adjusting the amount of information loss tolerated by the targeted applications. Our extensive experiments conducted on various real and synthetic graphs show that our sparsification considerably reduces the size of the graphs by achieving 40% sparsification rate on average on several input graphs. Furthermore, in the experimental study we show the utility and efficiency of our sparsification algorithm for notable data-driven tasks, such as node classification, graph classification and shortest path approximations. The obtained results exhibit interesting trade-offs between the runtime speed-up and the precision loss.