scale-dependent interaction rule is usually adopted, called the nearest-neighbor interaction rule [18]. The mechanism of the interaction network depends on communication radius. Inspired by natural starlings, a flocking algorithm with the combination of a consensus and artificial potential field has been proposed to reveal the underlying mechanism responsible for the emerging collective behaviors that a set of individuals move in unison while creating a dynamic formation pattern. The flocking control of wheeled mobile robots [19] and underwater robots [14; 20] were dealt with, yet these studies just considered the two-dimensional motion of individuals. [PERSON] et al. have studied the three-dimensional flocking of UAVs governed by a nonlinear dynamic model, but did not give any further analysis and discussion on how to accelerate the emergence of flocking behaviors and how to apply the proposed control algorithm to large-scale systems [21]. The second category uses a statistical method to analyze the simulation results. These simulations are designed mostly according to the real experimental data of flocks of animals. [PERSON] et al. have tracked and analyzed the movements of these starling flocks [22]. In this study, they found that there is not any leader in the colony. Besides, the number of individual birds in a flock can be as many as thousands, although each bird just follows local rules and only interacts with six to seven neighbors. Generally speaking, bigger interaction networks (referring to more interactions) yield faster consensuses. However, starlings show fast and flexible dynamic aggregation relying only on small interaction networks. Therefore, a problem exists in how the scale of the interaction network influences the emergence behavior of a flock. As proposed by economists, [PERSON] et al. found a phenomenon called diminishing returns, which led by the increasing of the number of deployed robots [23]. [PERSON] et al. also found that additional robots usually produce negative returns after a peak in performance when they focused on the scalability study of foraging tasks [24]. Besides, [PERSON] et al. have compared three strategies for aerial swarm deployment task according to the energy-time efficiency by using statistical analysis methods [25]. In this paper, a statistical method is applied to analyze whether the diminishing returns exist in the interaction network of an aerial swarm or not. According to the above research results, rigorous theoretical analysis can offer rigorous mathematical proof, but these conclusions are always limited to some unreasonable hypothesis. At the same time, although simulation can be carried out as close as possible to realistic conditions, these conclusions are easily doubted and argued because of some special cases. Therefore, our goal here is to design a general methodology and framework for studying flocking behaviors by means of the combination of control theory and statistical method. First, the UAV system is considered to be an egalitarian one with two basic properties: One is that every individual obeys the same control protocol to adjust its behavior during the entire process of flight, and the other is that each UAV uses the same communication radius to recognize its neighbors for information exchange. Thus, the communication radius can be regarded as the only factor to draw the scale of the interaction network. Second, a flocking protocol is proposed for each UAV to form a three-dimensional cohesive configuration in a consistent pattern. Instead of a simple first-order or second-order integrator, each UAV is simplified as a nonlinear dynamic model commonly used to describe the UAV in the existing literature [26; 27]. According to the LaSalle-Krasovskii invariance principle [28], the UAV flocking will emerge as long as the initial interaction network is connected. During the evolutionary process, collision is carefully avoided among pairwise UAVs.