Shortest path computation is one of the most fundamental operations for managing and analyzing large social networks. Though existing techniques are quite effective for finding the shortest path on large but sparse road networks, social graphs have quite different characteristics: they are generally non-spatial, non-weighted, scale-free, and they exhibit small-world properties in addition to their massive size. In particular, the existence of hubs, those vertices with a large number of connections, explodes the search space, making the shortest path computation surprisingly challenging. In this paper, we introduce a set of novel techniques centered around hubs, collectively referred to as the Hub-Accelerator framework, to compute the k-degree shortest path (finding the shortest path between two vertices if their distance is within k). These techniques enable us to significantly reduce the search space by either greatly limiting the expansion scope of hubs (using the novel distance- preserving Hub-Network concept) or completely pruning away the hubs in the online search (using the Hub2-Labeling approach). The Hub-Accelerator approaches are more than two orders of magnitude faster than BFS and the state-of-the-art approximate shortest path method Sketch for the shortest path computation. The Hub- Network approach does not introduce additional index cost with light pre-computation cost; the index size and index construction cost of Hub2-Labeling are also moderate and better than or comparable to the approximation indexing Sketch method.