The resource constraint is one of the top issues in the Internet of Things network. All activity in the network node should be carefully designed and managed to support the resource efficiency of the network. Hence, an energy efficient transceiver like ZigBee is popularly used as the infrastructure for the Internet of Things edge network. This paper presents our method for efficient ZigBee router node deployment which minimizes the number of communication hop in ZigBee based network in an area of implementation. The method aims to construct a ZigBee network tree topology with the minimum number of ZigBee routers while providing communication service to all points of interest. We use a virtual grid to transform the problem into a graph problem. The Physarum optimization algorithm is used to determine the minimum number and the position of the routers, according to the gateway and point of interest locations. The validation to the method is carried out using Matlab simulation. The simulation result shows that the algorithm can successfully meet the requirement with the accuracy level of as low as 93.64%. It also shows that there is a tradeoff between degree of accuracy and computation time. The increase in grid spacing will increase the computation time exponentially, while the increase in the number of point of interest will increase the computation time linearly.