||Recent years have seen significant advances in directional antenna technologies, and the beginnings of deployment of directional antennas into wireless networks. A directional antenna is capable of concentrating its transmission energy within a narrow angle, aimed in an intended direction. Our research is centered on the following question: Can we provide each node with multiple directional antennas, and configure these antennas appropriately to form efficient communication graphs? Our main goal is to analyze the suitability of Yao graphs as communication graphs for networks with directional antennas. One could associate an antenna with a Yao sector. For a small number of sectors, Yao graphs are known to perform poorly under fixed sector orientation. We allow each node to orient its own sectors (and therefore antennas) independent of other nodes, and evaluate these graphs empirically under arbitrary sector orientation at each node. Motivated by connectivity issues in wireless networks, we also investigate the following theoretical problem: What is the minimum radius d for which Y k [d] is connected (for small values of k and d)? These are some of the questions we are exploring in this thesis.