Throughput scaling laws of an ad hoc network equipping directional antennas at each node are analyzed. More specifically, this paper considers a general framework in which the beam width of each node can scale at an arbitrary rate relative to the number of nodes. We introduce an elastic routing protocol, which enables to increase per-hop distance elastically according to the beam width, while maintaining an average signal-to-interference-and-noise ratio at each receiver as a constant. We then identify fundamental operating regimes characterized according to the beam width scaling and analyze throughput scaling laws for each of the regimes. The elastic routing is shown to achieve a much better throughput scaling law than that of the conventional nearest-neighbor multihop for all operating regimes. The gain comes from the fact that more source--destination pairs can be simultaneously activated as the beam width becomes narrower, which eventually leads to a linear throughput scaling law. In addition, our framework is applied to a hybrid network consisting of both wireless ad hoc nodes and infrastructure nodes. As a result, in the hybrid network, we analyze a further improved throughput scaling law and identify the operating regime where the use of directional antennas is beneficial.