## 5 Characteristics Analysis with Uniform Node Distribution  
In this section, the characteristics analysis with uniform node distribution is presented. In a network with identical node density, the node degree will affect transmission range and energy efficiency. The transmission range must be adjusted when nodes have to alter degree to achieve optimal connection quality. The node with less degree requires lower transmission power. The node of less degree easily leads to an interruption of the delivery route for a network. In order to maintain the transmission route between node pairs, the transmission range of a node should be increased to facilitate connection with adjacent nodes and provide the possibility of route selection. On the contrary, longer transmission range is necessary to add degree of node but needed power is higher. More node degree will provide more possibility of route selection. However, redundant node degree maybe causes the channel interference. Hence, a proper node degree is extremely valuable for network performance. An optimal transmission range is obtained by proposed adjustment model. A full reachability network with minimum node degree will be built by this optimal transmission range. This optimal transmission how to transform to needed power depends on the chip design. This issue has to be considered in real operation. However,in this study, the proposed mathematical model focuses on theoretical analysis. And the analyzed results will benefit the future deployment of real applications. Next, the case of a network with different node densities will be discussed. In real applications, node density must be determined first. The distance between nodes is different according to node density. The distance between nodes in low node density is longer than that between nodes in high node density. Hence, the needed transmission power in low node density is higher than that between nodes in high node density under the same node degree. In other words, where node degrees are identical, and each node has to meet this requirement, a network with low node density requires a longer transmission range and higher transmission power than does one with high node density. In addition, the distance between nodes will be closer when node density continuously increases. Accordingly, in a network with high node density, a fixed transmission range can simultaneously satisfy different conditions of node degree. Therefore, the transmission range is not easily influenced by node degree in a network with high node density. This fact indicates that a network with high node density is more efficient to improve energy efficiency. By contrast, the node degree easily influences the transmission range of the nodes in a network with low node density. There are two performance indices to evaluate the connection quality of network. In this paper, connectivity and reachability are defined according to the directness or indirectness of the route between nodes in a network, respectively. If a node wants to deliver data to a distant node, the power consumption required by direct transmission is higher than that required by indirect transmission. Therefore, a network with full connectivity requires more power than does a network with full reachability. According to the simulation results of Section 4, a network with high node density will improve energy consumption of nodes efficiently. Because of the distance between close nodes is shorter, the needed power for delivery is lower. Hence, each node only connects with adjacent nodes through adjusted transmission range with a proper node degree. This proper node degree has to guarantee to establish a full-reachability network. In this way, the connection of node with far node only needs less power due to indirect delivery. In addition, a network with low node density is difficult for establishing full-reachability network topology.