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FONT face=Verdana>Topology control aims to maintain network connectivity and reduce energy consumption for Ad hoc networks using steered beam directional antennas. To derive analytical expressions to determine the critical transmission range and neighbor number K

we employ quadrat statistical methods. A distributed neighbor-based topology control approach

referred to as the DK-Neigh

is proposed to maintain the outdegree of every node equal to or slightly below a specific value K. The approach can build the resulting communication graph with high probability connected. Extensive simulations are carried out

which show that the DK-Neigh is to achieve a high probability (more than 96%) of connectivity. If width of beam is smaller than 60

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average energy cost of nodes is reduced at least 15% than the topology control protocol K-Neigh using omni-directional antennas. Simulations show the DK-Neigh is more

energy-efficient while maintaining network connectivity.