*4.2. Network Size*

Figure 11 shows the average of the power consumption, hop count and degree while varying the number of the UAVs from 20 to 100. We compared the case of FC, SMST, and TC-4 for each performance metric. The other parameters for the simulations are set as default, listed in Table 1. As shown in Figure 11a, TC-4 shows higher decrement ratio of the power consumption than the other cases. This is due to the unique property of the topology control layer, which adopts the transmission power of each link, while sustaining the number of the nearby links. Increasing the number of the UAVs leads to the decreases of the average distances between the UAVs. In the case of SMST, this decrement results in the low transmission power of the links just as TC-4, due to centralized topology generation. However, due to the properties of the minimum spanning tree, higher density of UAVs inevitably causes higher hop counts, which is shown in Figure 11b. As mentioned before, increasing hop count consequently increases the power consumption of the end-to-end connection, which results in relative inefficiency as in Figure 11a. On the other hand, the case of FC sustains smaller hop count and larger degree (Figure 11c) than the other cases, but it has much higher power consumption due to the fixed and excessive amount of the transmission power. Furthermore, a larger degree of UAVs indicates higher robustness, but also brings the potential for more congestion and the collision of the frames. Figure 11c shows that the case of FC steadily increases the degree of UAVs, which leads to the degradation of the throughput and the efficiency of the transmission. In summary, the results in Figure 11 proved that the topology control layer yields a moderated degree and hop count, which results in it outperforming the power efficiency of the UAV network.

**Figure 10.** Network topology of a random formation while varying *n*. (**a**) FC network topology of random formation; (**b**) SMST network topology of random formation; (**c**) TC-2 network topology of random formation; (**d**) TC-4 network topology of random formation; (**e**) TC-8 network topology of random formation; (**f**) TC-20 network topology of random formation.

**Figure 11.** Numerical results while varying the number of UAVs. (**a**) Average power consumption; (**b**) Average hop count; (**c**) Average node degree.

#### *4.3. Number of Partitions*

We also measured the results while varying the number of the partitions, where *n* = {2, 4, 6, 8, 12, 20}. As shown in the subfigures in Figure 12, the cases of TC-*n* outperform the other cases (FC, SMST) in power consumption. In the case of the hop count and the degree, TC-*n* shows the medium values between the FC and the SMST, since the topology control layer prunes the links regarding to the number of the partitions. On the other hand, as *n* increases, hop count decreases and the degree increases. Due to the increase of the possible links in larger *n*, there are more chances to decrease the hop count with the larger number of partitions. Furthermore, it is notable that the average power consumption of end-to-end connection is minimum at *n* = {6, 8}, regardless of the number of the UAVs. However, it is hard to conclude that the network is *optimal* at a certain *n*, since the larger *n* results in lower hop count, which leads to the improvement of the expected throughput. In conclusion, the results in Figure 12 show that there is an optimal *n* value for the desired objective of the UAV network.

**Figure 12.** Numerical results while varying *n*. (**a**) Average power consumption; (**b**) Average hop count; (**c**) Average node degree.
