*4.1. Regular Formations*

To effectively show the resulting shape of the network topology of our system, we first conducted the evaluation with the regular formation of the UAVs, such as grid-shape or sphere-shape. Figure 8 shows the three-dimensional representation of each network topology. In the case of the grid formation, we deployed 4 × 4 × 4 UAVs with the default size of the map space, and the same distance of the width, height and depth between the nearby UAVs. In the case of the sphere formation, we deployed 66 UAVs in the surfaces of 3 concentric spheres. As shown in the Figure 8a, if all UAVs fully connect to the nearby UAVs in its maximum transmission range, the topology gets highly complex and this may lead to high interference in the wireless medium. On the other hand, the case shown in Figure 8b shows an MST including the network, which could lead to the high hop count of some connections, such as the route from 51 to 46, which has 17 hops. The topology result of our proposed topology control layer is shown in Figure 8c, which represents visually expected connections at this grid formation. The reason for the result is that the topology control layer only leaves the nearest link from each partition. While the fully connected cases in Figure 8a,d suggest the intensive traffic on the center of the network, the TP-6 cases in Figure 8c,f reduce this potential by filtering the further connections of each UAV and controlling the transmission power of each link. As shown in the topologies in Figure 8, we showed how our proposed system forms the topology of the UAV network, compared to the other comprehensive or centralized methods.

**Figure 8.** Network topologies in regular formations. (**a**) FC network topology of grid formation; (**b**) SMST network topology of grid formation; (**c**) TC-6 network topology of grid formation; (**d**) FC network topology of concentric spheres formation; (**e**) SMST network topology of concentric spheres formation; (**f**) TC-6 network topology of concentric spheres formation.

Figure 9 shows the evaluation results of the network topologies shown in Figure 8. We measured the average and the confidence interval of the power consumption, hop count of end-to-end connections, and the node degree of the UAVs. As shown in Figure 9a, TC-6 outperforms the other cases FC and SMST, while showing less than a half of the power consumption of the other cases. It is remarkable that TC-6 shows much less power consumption than SMST, which grants centralized optimal topology of the whole UAV network. The reason for this outperformance is mainly due to the advantage in the hop counts (Figure 9b), since larger hop count of the SMST case leads to more frequent transmissions, which incurs the large amount of the power consumption despite the low transmission power. By numerical comparison, we showed our proposed topology control layer can reduce the power consumption of the UAV network, through the efficiently constructed network topology. In the following graphs, for better visibility, we omitted the confidence interval of the results, which shows almost similar tendencies to the remaining evaluations.

**Figure 9.** Numerical results in regular formations. (**a**) Average power consumption; (**b**) Average hop count; (**c**) Average node degree.

To show the differences in the network topology while varying *n* at the general case, we ran our proposed system in a random formation, as shown in Figure 10. In this figure, we deployed 20 UAVs in the map with uniform random distribution. As shown in the subfigures, when *n* increases, the shape of the network topology gets closer to the FC case, as TC-20, shown in Figure 10f. Please note that UAVs select at most *n* UAVs as their next hops in each partition, which has smaller size at larger *n*. The case of larger *n* has more chance to grab the UAVs in the transmission range as their next hops, so larger *n* acts as similar to the FC case. However, the expected power consumption of the end-to-end connection is smaller than the FC case even though larger *n* cases, since topology control layer designates the transmission power of the links. In the following subsections, we evaluate our system while varying the numerical parameters, to show how the parameters affect the performance of the topology control layer.
