A Quality Evaluation Method for Drone Swarm Command and Control Networks Based on Complex Network

Highlights

What are the main findings?

• A network modeling and quality assessment method for drone swarm command and control (C2) systems based on complex networks has been proposed. This method effectively evaluates the advantages and disadvantages of drone swarm C2 structures as well as their mission adaptability from a topological perspective. The evaluation framework can serve as a reference for analyzing and evaluating other combat systems.
• Taking same-scale networks with different C2 structures as the basis for case analysis, this study demonstrates that the three types of distributed C2 structures each have their own advantages and disadvantages under different scenarios, such as static scenarios, random attacks, and targeted attacks. The dynamic network evaluation further demonstrates the universality of the evaluation method for networks with different structures, which can be used to guide the design of C2 system architectures.

What is the implication of the main finding?

• Complex networks can accurately characterise the structure of the drone swarm C2 system. Through network modeling of the drone swarm C2 system, complex network theory can be used to effectively analyze the system. The method can be applied to research on other complex combat systems.
• The Leader–Follower-based network exhibits good performance in terms of static structure and under random attacks, but has the worst performance under targeted attacks. It is suitable for long-endurance, long-range tasks such as security patrols and reconnaissance surveillance, as well as large-scale deployment scenarios, but not for combat missions involving high confrontation. Although the BA network and ER network have relatively poor performance in terms of static structure and under random attacks, they perform better under targeted attacks; in particular, the ER network structure is most suitable for high-confrontation tasks.

Abstract

To address the issues of structural diversity, modeling complexity, and the lack of evaluation methods in drone swarm command and control (C2) networks, this paper proposes a complex network-based quality evaluation method for drone swarm C2 networks from a network topology perspective. First, by analyzing the structure of the drone swarm C2 system, three hierarchical C2 network models are constructed, which are based on the Leader–Follower architecture, BA scale-free network, and ER random network, respectively. Subsequently, a drone swarm network quality evaluation indicator, system integrating network connectivity, load status, and transmission efficiency is established, along with an evaluation model that considers both static and dynamic characteristics. Finally, an analysis is conducted using networks of the same scale but different C2 structures. The evaluation results demonstrate that this method can effectively distinguish the performance of networks with different structures and exhibits good applicability under both random and targeted attack scenarios. Under static scenarios, distributed C2 networks exhibit the highest quality values, while centralized networks demonstrate the lowest. In random attack scenarios, the Leader–Follower structure achieves the highest network quality among the three hierarchical architectures, outperforming BA and ER network structures by 117% and 25%. In targeted attack scenarios, the ER network structure achieves the highest network quality, surpassing Leader–Follower and BA network structures by 66% and 17%. It provides a quantitative reference for the design and optimisation of the drone swarm C2 system structure.

1. Introduction

As an emerging operational mode, drone swarm operations have significant research space and development potential [1]. A C2 network is a network model abstracted from the C2 system, formed by entities connected through communication links [2]. The quality evaluation of drone swarm C2 networks serves as the foundation for the design of the drone swarm C2 system. It helps technicians gain a more comprehensive understanding of the relationship between the structure and effectiveness of the drone swarm C2 system, exploring ways to maximise large-scale collaborative effectiveness [3].

1.1. Related Work

Since the advent of network science in the early 21st century, complex network theory has greatly advanced the analysis of complex systems through a unified theoretical framework [4]. Complex network theory has been proven to be a scientific method for modeling and analyzing complex systems [5], and has been widely applied in fields such as transportation systems [6,7,8], ecological systems [9,10,11], and power systems [12,13,14]. The prerequisite for analyzing a system using complex network theory is to construct a network that is consistent with the real system. Therefore, in-depth analysis of the research object’s characteristics, functions, and properties is required. For example, Hu et al. proposed a drone swarm network model that combines distance and node degree to characterise the drone swarm network, aiming to quantitatively evaluate the robustness of the drone swarm system [15]; Wang et al. constructed a two-layer, three-mode supernetwork for analyzing the capability of regional air defense operation systems, which can effectively identify key nodes of the system and evaluate system effectiveness [16]. Currently, there are studies on drone swarm networks [17,18,19], but relatively little research on drone swarm C2 networks, leading to insufficient understanding of their structures. Given the diversity of drone swarm C2 systems, research on drone swarm C2 networks must be based on in-depth analysis of the C2 system architecture and use appropriate network models for modeling.

Numerous scholars at home and abroad have applied complex network theory to the evaluation of complex systems. Some scholars have developed evaluation models based on general indicators derived from complex network theory. For instance, Fan et al. built an evaluation model using parameters such as degree distribution, average path length, and clustering coefficient, which was applied to evaluate the communication capability of manned/unmanned aerial vehicle (MAV/UAV) collaborative systems [20]; Zhang et al. focused on the resilience evaluation of drone swarm networks, simulated physical damage and communication interruptions by removing nodes and edges, and constructed an evaluation model using network topological indicators such as average degree and clustering coefficient [21]. Other scholars have defined new indicators based on complex network theory and combined them with system characteristics for research on specific network models. For example, Yang et al. proposed five new indicators, including node integrity, hub node function, and hub edge function, to address the vulnerability evaluation of MAV/UAV collaborative operation networks [22]. They determined weights based on multiple correlation coefficients and aggregated the indicator values to obtain evaluation results; Sun et al. combined the operational loop theory and used the number of generalized operational loops and their weights as measurement indicators for evaluating the effectiveness of operational networks [23]. Due to insufficient research on C2 structures, most of these network analysis indicators are poorly aligned with the performance of C2 systems. It is therefore necessary to develop a scientific and appropriate indicator system that integrates the characteristics of the drone swarm C2 system.

When drone swarm perform missions, they are vulnerable to interference or attacks, leading to drone malfunctions, communication interruptions, and subsequent dynamic changes in their network structures. Therefore, the evaluation of the C2 systems cannot be limited to static structures. For example, Wang et al. evaluated the robustness of drone swarm based on complex network theory, analyzed and modeled the dynamic evolution of drone swarm under attacks, and established an evaluation model with a comprehensive robustness indicator [24]; Wei et al. used the Susceptible-Infected-Susceptible (SIS) model to simulate communication link failures when drone swarm is subjected to electronic jamming attacks, studied the resilience of drone swarm networks, and proposed a resilience enhancement model for drone swarm [25]; Zhang et al. simulated attack intensity through node failure probability, studied the load balancing issue of drone swarm after being attacked, and analyzed the impacts of different topological structures and parameters on the recovery capability of drone swarm [26]. From an application perspective, research on the performance of C2 systems should conduct dynamic analysis alongside application scenarios and explore the relationship between C2 systems and mission requirements [27]. Building on the achievements of existing complex network evaluation methods, insights can be provided for the quality evaluation of drone swarm C2 networks.

1.2. Motivations

Through a literature review of relevant studies, the main shortcomings of existing research are summarized as follows: (1) Existing studies on drone swarm network modeling pay insufficient attention to C2 system networks. The relevant network models have not fully modeled the hierarchical and heterogeneous characteristics of the drone swarm C2 system, and thus fail to accurately characterize the structure of the drone swarm C2 system. (2) The existing evaluation indicators for drone swarm networks focus on the network structure itself and fail to fully connect with the core functions of the C2 system. (3) The existing evaluation frameworks generally target static topological structures, involve little analysis of robustness in adversarial environments, and cannot reflect the dynamic changes of the drone swarm during mission execution.

The quality evaluation of the drone swarm C2 network is not only fundamental research for realizing the large-scale benefits of drone swarm, but also forward-looking research for the practical application of future drone swarm. Currently, there is an urgent need for a scientific method for evaluating the quality of the drone swarm C2 network.

1.3. Contributions

Focusing on the quality evaluation of drone swarm C2 networks, this paper proposes a quality evaluation framework based on complex networks, following an in-depth analysis of the drone swarm C2 system structure. The main work is as follows:

• Corresponding network models are constructed respectively for the centralized, distributed, and hierarchical drone swarm C2 structures. For the hierarchical C2 structure, three network models—based on leader–follower, BA scale-free network, and ER random network—are proposed, which accurately characterize the structural features of the drone swarm C2 system.
• Combining the characteristics of the drone swarm C2 system, an evaluation indicator system for drone swarm network quality is established, which comprehensively reflects the network topological structure of the drone swarm C2 system.
• A drone swarm C2 network quality evaluation model based on complex networks is constructed, and an evaluation method that considers both the static and dynamic aspects of the C2 system is proposed. This enables a comprehensive evaluation of the structural performance of the drone swarm C2 system.
• Through evaluation experiments on the quality of drone swarm C2 networks with different structures under the same scale, the feasibility and effectiveness of the evaluation method are verified, and the mission adaptability of different C2 structures is analyzed.

The structure of this paper is organised as follows: Section 2 analyzes the structure of the drone swarm C2 system and proposes modeling methods for C2 networks with different architectures. Section 3 establishes a quality evaluation indicator system for drone swarm C2 networks based on complex networks, as well as a static and dynamic dual-dimensional evaluation method. Section 4 designs simulation experiments, constructs typical networks for comparative analysis, and verifies the adaptability and discriminability of the proposed model under different topological structures. Section 5 summarizes the content of the paper.

2. Network Modeling Method

2.1. Structure of the Drone Swarm C2 System

The C2 system is a hierarchical system centered on command levels and resource scheduling methods, supporting operational command decisions, information interaction, and battlefield control. It is one of the key components in operational system design and operational concept research. Currently, the C2 system structures of drone swarm mainly include three types: centralized, distributed, and hierarchical [28], among which the hierarchical structure can be further divided into various subtypes such as Leader–Follower-based, BA scale-free network-based and ER random network-based structures. The schematic diagrams of the drone swarm C2 structures are shown in Figure 1.

(1) Centralized C2 Structure

The centralized C2 structure is currently the most widely used and mature swarm C2 structure, where a single ground station is directly connected to and controls multiple drones. Its structural schematic is shown in Figure 1a. Its advantages lie in simple control logic: only the central node needs to uniformly schedule the drone swarm, resulting in strong task controllability. However, it is limited by a single control center, making it difficult to adapt to large-scale swarm control. With the increasing demand for large-scale and intelligent drone swarm, as well as the rising complexity of tasks, the limitations of the traditional centralized C2 architecture have become increasingly prominent. The centralized C2 network features a simple structure, consisting of a single command node connected to multiple unmanned aerial vehicle nodes. There is no interconnection between nodes, forming a star-coupled network.

(2) Distributed C2 Structure

The distributed C2 structure has no central node. Adjacent drones achieve global autonomous collaboration through local information exchange, without the need for external command and control, thereby realizing “decentralization”. Its structural schematic is shown in Figure 1b. However, it has the disadvantages of extremely high control complexity and weak controllability. Moreover, at the current stage, drones can hardly achieve globally optimal decisions relying solely on local information. Due to various technical bottlenecks in distributed control, it is still difficult to apply this structure in drone swarm of a certain scale. The distributed C2 network architecture is equally simple, lacking dedicated command nodes. All unmanned aerial vehicle nodes are interconnected, forming a globally coupled network.

(3) Hierarchical C2 Structure

The hierarchical C2 structure adopts the idea of hierarchical structure to address problems, which is an effective means to solve the complexity of multi-drone collaborative control and system architecture. The core of hierarchical control is to stratify command, decision-making, and strike functions. drones with high intelligence are used as leader nodes, which are uniformly commanded by the C2 center. Within the swarm, the leader nodes make decisions to allocate tasks and coordinate dynamically. The hierarchical C2 structure combines the advantages of centralized and distributed C2 structures, balancing feasibility and technological advancement, and has become a research focus in the control of large-scale drone swarm [29].

2.2. Drone Swarm C2 Network Modeling

Based on the drone swarm C2 architecture, drone swarm C2 networks can be categorized into centralized, distributed, and hierarchical networks. Among these, centralized C2 networks are star-coupled networks, distributed C2 networks are globally coupled networks, while hierarchical command networks feature complex and diverse architectures that are not confined to a single network model.

(1) Leader–Follower-based Hierarchical C2 Network

The “Leader–Follower” architecture is a classic hierarchical control framework. Its core idea is to designate one or more agents with high intelligence as leaders in the swarm, while the remaining agents serve as followers. Typically, in such a network, there are connections between leaders and between followers connected to the same leader, forming several subgroups. Its structural schematic is shown in Figure 1c. The leaders guide the followers in flight, allocate tasks, and make decisions, enabling the entire swarm to fly in formation and perform tasks in a collaborative manner.

(2) BA Scale-Free Network-based Hierarchical C2 Network

A BA (Barabási–Albert) scale-free network is characterized by a power-law degree distribution, with a small number of high-degree nodes and a large number of low-degree nodes. In the drone swarm C2 network, ground control stations and leader drone nodes need to undertake more functions such as forwarding command instructions and task allocation, naturally forming the topological characteristic of “few core nodes with many ordinary nodes”. The power-law distribution characteristic of BA networks precisely simulates the actual behavior of newly added sub-drones in a swarm deployment, where they prioritize connecting to leader nodes or command stations with broader communication coverage and stronger computational power [30]. This aligns with the tactical logic of hierarchical command and control, where core nodes dominate command operations. Assuming the degree of node S is $k_s$, the probability that a new node connects to S is

$$p\left(k_s\right)={\displaystyle \frac{k_s}{{\displaystyle \sum _{i=1}^n}{k}_i}}$$

(1)

The hierarchical C2 network based on the BA scale-free network takes the BA model as the underlying topology and constructs a hierarchical command structure dominated by hub nodes. Its structural schematic is shown in Figure 1d. Its core is to utilize the power-law degree distribution characteristic of the BA network: select a small number of nodes with dense connections as hub nodes and most ordinary nodes with sparse connections, and use the hub nodes as the core of the hierarchical command to achieve efficient command and control and anti-destruction capabilities for large-scale swarm.

(3) ER Random Network-based Hierarchical C2 Network

An ER (Erdős–Rényi) random network is one in which the connection probability between nodes is fixed, nodes within the same level are randomly connected, and information is transmitted between levels via fixed channels. In actual drone missions, communication distance, terrain obstructions, and electronic interference cause random variations in connections between peer-level leader nodes and between leaders and subordinate drones. A leader drone usually only connects to several drones closest to it, and the connections between leader drones are also random [31]. To construct a network under such circumstances, the hierarchical C2 network based on the ER random network model can be built by setting the connection probability between leader drones $p_{LL}$, the connection probability between leader drones and sub-drones $p_{LS}$, and the connection probability between sub-drones $p_{SS}$. Its structural schematic is shown in Figure 1e. The modeling approach for the “fixed connection probability” in ER networks accurately captures the uncertainty in drone-to-drone connections during actual mission execution, consistent with the dynamic randomness of drone communications in real battlefield environments.

Based on the construction of network models, an evaluation model is further established to evaluate the quality of the drone swarm C2 network, thereby realizing the analysis of the performance and mission adaptability of different C2 systems. The overview of the proposed framework is shown in Figure 2.

3. Evaluation Model

3.1. Network Quality Evaluation Indicator System Based on Topological Structure

The network quality evaluation metric system must encompass network connectivity, network load status, and network transmission efficiency. Network connectivity represents the “physical foundation” of the network; for large-scale and highly mobile drone swarm, maintaining good connectivity is a prerequisite for performing any collaborative tasks [28,32]. Network load status reflects the “resource state” of the network [33]. For drone swarm with dense nodes and frequent communication, load balancing is crucial for maintaining network performance. Network transmission efficiency embodies the “command and control response speed”, directly reflecting whether the network can meet the information transmission requirements of drone swarm tasks [34]. These three evaluation dimensions cover three aspects of drone swarm C2 network quality: network connectivity reflects the network’s structural quality, load status reflects the network’s state quality, and transmission efficiency reflects the network’s task execution quality. The indicators are further decomposed to construct a three-level quality evaluation indicator system for the drone swarm C2 network, as shown in Figure 3.

3.1.1. Network Connectivity

(1) Average node degree K

The average node degree is the average number of connections per node in the network. It measures the connection density or global activity of the network and is a positive indicator, as expressed in Equation (2). Where N denotes the total number of nodes in the network, and $k_i$ represents the degree of node i. The average node degree directly reflects a network’s command coverage capability. A higher K value indicates that a single drone can connect to more collaborative nodes, meaning richer parallel paths for command transmission. Tactically, this corresponds to faster multi-node coordinated response speeds and reduces command delays caused by single-point communication blockages.

$$K={\displaystyle \frac{1}{N}}\sum _{i=1}^N{k}_i$$

(2)

(2) Average clustering coefficient C

The average clustering coefficient measures the tightness of connections between the neighboring nodes of a node in the network, reflecting the local aggregation or “clustering” degree of the network. It is a positive indicator with a value range of $[0,1]$, as shown in Equation (3), where M represents the total number of edges in the network. The average clustering coefficient characterizes a network’s local collaborative tightness. A higher C value indicates tighter connections among nodes at the same level, tactically corresponding to high efficiency in local task coordination and reduced reliance on cross-level instructions.

$$C={\displaystyle \frac{1}{N}}\sum _{i=1}^N{\displaystyle \frac{2M}{k_i(k_i-1)}}$$

(3)

(3) Network density $\rho$

Network density is the ratio of the actual number of edges in the network to the maximum possible number of edges. It is a direct measure of the overall connection tightness of the network and is a positive indicator with a value range of $[0,1]$, as expressed in Equation (4). Network density reflects the level of redundant connections within a network. A high $\rho$ value indicates a tactical avoidance of command link vulnerabilities caused by insufficient density.

$$\rho ={\displaystyle \frac{2M}{N(N-1)}}$$

(4)

3.1.2. Network Load Status

(1) Load Gini coefficient G

The Gini coefficient is a classic indicator for measuring the fairness of resource allocation. It is a negative indicator with a value range of $[0,1]$, where 0 indicates complete balance (all nodes have the same degree) and 1 indicates complete imbalance (all loads are concentrated on one node). Let $k_i^{\prime }$ be the node degrees sorted in descending order, i.e., $k_1^{\prime }\le k_2^{\prime }\le \dots \le k_N^{\prime }$. The horizontal axis of the Lorenz curve is set as the proportion of cumulative nodes ${\displaystyle \frac{j}{N}}$, and the vertical axis is the proportion of cumulative degrees. The Gini coefficient is expressed as the ratio of the area between the Lorenz curve and the line of absolute equality to the area under the line of absolute equality in the coordinate system. In practical calculations, it can be approximated using a discrete equation, as shown in Equation (5). The load Gini coefficient reflects the balance of command load distribution. A lower G value indicates more even distribution of command tasks across nodes, tactically preventing core node overload and failure while enhancing the C2 system’s sustained operational capability.

$$G={\displaystyle \frac{2{\sum }_{i=1}^{N}i·k_i^{\prime }}{N·{\sum }_{i=1}^N{k}_i^{\prime }}}-{\displaystyle \frac{N-1}{N}}$$

(5)

(2) Social node ratio R

The social node ratio is the ratio of the number of nodes with the highest degree to the total number of nodes in the network. It is used to measure the concentration of “hub” nodes in the network and is a positive indicator with a value range of $[0,1]$, as expressed in Equation (6). Where $N_{max}$ denotes the number of nodes with the maximum degree. The social node ratio characterizes the degree of decentralization within the command core. A higher R value indicates a greater number of high-degree nodes, tactically corresponding to decentralized command authority. This reduces reliance on a single leader drone node and enhances the network’s robustness against the destruction of core nodes.

$$R={\displaystyle \frac{N_{max}}{N}}$$

(6)

(3) Node assortativity coefficient $\tau$

The node assortativity coefficient measures the tendency of high-degree nodes in the network to connect with nodes of a certain degree. It is a positive indicator with a value range of $[-1,1]$. A value of $\tau <0$ indicates disassortativity (connections between high-degree and low-degree nodes), meaning the degree distribution tends to be unbalanced; a value of $\tau >0$ indicates assortativity, meaning the degree distribution tends to be balanced. Tactically, this means establishing a command backbone network between core nodes to enhance the priority and efficiency of command transmission. According to the Pearson correlation coefficient equation $\tau ={\displaystyle \frac{Cov(X,Y)}{{\sigma }_X{\sigma }_Y}}$, let X and Y be the sets of degrees of the left and right endpoints of all edges, respectively. Let $(i,j)$ represent any edge in the network, and $k_i$ and $k_j$ represent the degrees of the left and right endpoints, respectively. The calculation equation of $\tau$ can be derived as shown in Equation (7).

$$\tau ={\displaystyle \frac{M^{-1}{\sum }_{i=1}^M{k}_i{k}_j-{\left(M^{-1}{\sum }_{i=1}^M\frac{k_i+k_j}{2}\right)}^2}{M^{-1}{\sum }_{i=1}^M\frac{k_i^2+k_j^2}{2}-{\left(M^{-1}{\sum }_{i=1}^M\frac{k_i+k_j}{2}\right)}^2}}$$

(7)

3.1.3. Network Transmission Efficiency

(1) Network efficiency E

Network efficiency is an indicator for measuring the global efficiency of information or resource transmission in the network. It is expressed as the average of the reciprocals of the shortest path lengths between all pairs of nodes and is a positive indicator, as shown in Equation (8). Where $d_{ij}$ represents the shortest path length between node i and node j. Network efficiency directly reflects command response speed. A higher E value indicates a shorter minimum path between nodes, resulting in lower tactical command latency from the command station to the executing drones.

$$E={\displaystyle \frac{1}{N(N-1)}}\sum _{i,j=1,i\ne j}^N{\displaystyle \frac{1}{d_{ij}}}$$

(8)

(2) Throughput T

Throughput refers to the total amount of valid commands or data successfully transmitted from the ground control station to all subordinate drones via the Leader drone within a unit of time in a hierarchical C2 network for drone swarms, as shown in Equation (9). In the equation, a $N_S$ denotes the number of sub-drone nodes, $E_{0l}$ and $E_{lj}$ represent the number of edges from the control station node to the leader nodes and from the leader nodes to the sub-drone nodes respectively, $H_{0j}$ indicates the number of paths from the control station to the j sub-drone, and its coefficient quantifies the suppression of transmission by node load. $k_0$ and $k_l$ denote the degree of the control station nodes and the leader drone nodes respectively. Its fundamental meaning is the command distribution capacity of the drone swarm C2 system, directly reflecting the network’s support limits for large-scale collaborative missions. Using a two-tiered link structure—from the ground control station to the leader drones and then to the sub-drones—as the transmission medium, this approach comprehensively considers key parameters such as the number of effective links in the topology, node load distribution, and the number of paths.

$$T={\displaystyle \frac{1}{N_S}}\sum _{j=1}^{N_S}\left[{\displaystyle \frac{E_{0l}+E_{lj}}{(1+\frac{k_0+k_l}{2K})·H_{0j}}}\right]$$

(9)

(3) Average delay L

Average delay refers to the total average time required for a command or task data packet to travel from the ground control station through the leader drones to all sub-drones in a hierarchical C2 network for drone swarms, as shown in Equation (12). The delay comprises transmission delay, processing delay, and propagation delay. Transmission and processing delays are positively correlated with the degree of the sending and processing nodes, respectively. Propagation delay is positively correlated with the degree difference between the sending and processing nodes. Parameters $\alpha$, $\beta$, ${\delta }_1$, and ${\delta }_2$ validated through simulation experiments, yield the closest approximation to actual delays when set to 0.5, 0.3, 0.2, and 0.1, respectively. Average delay serves as the core tactical metric for evaluating the real-time performance and reliability of command transmission in drone swarm C2 systems, directly determining the effectiveness, coordination precision, and survivability of drone swarm mission execution.

$$L={\displaystyle \frac{1}{N_S}}\sum _{j=1}^{N_S}[\alpha (k_0+k_l)+\beta (k_l+k_j)+{\delta }_1\left|k_0-k_l\right|+{\delta }_2\left|k_l-k_j\right|]$$

(10)

(4) Time delay jitter J

Time delay jitter is a dimensionless metric quantifying the fluctuation in end-to-end delay experienced by all sub-drones when receiving commands from the ground control station within a hierarchical C2 network for drone swarms, as shown in Equation (13). Its core principle lies in the ratio of maximum to minimum single-node delay, providing an intuitive reflection of the consistency in command arrival times across execution nodes. This fundamentally demonstrates the drone swarm C2 system’s capability for synchronized command distribution.

$$J={\displaystyle \frac{{max}_{1\le j\le N_S}\left(L_j\right)}{{min}_{1\le j\le N_S}\left(L_j\right)}}$$

(11)

3.2. Drone Swarm C2 Network Quality Evaluation Method

The evaluation of the quality of a drone swarm C2 network should be conducted in conjunction with its actual application requirements. The static structure reflects the fundamental architectural attributes of the C2 system, while the dynamic aspect reflects its adaptability in application scenarios. Analyzing network quality across both dynamic and static dimensions facilitates decision-making aligned with mission requirements. For example, in reconnaissance and surveillance missions, which have a long mission duration and low adversarial intensity, high stability of the static structure is required; in targeted strike missions, high network survivability and stronger dynamic adaptability are required; in large-scale, high-intensity adversarial mission environments, both static stability and dynamic adaptability must be considered. Therefore, for the network model of the drone swarm C2 system, after establishing an evaluation indicator system, corresponding evaluation models are proposed from both dynamic and static perspectives to evaluate the network quality value.

3.2.1. Static Evaluation Method

After calculating the values of the network quality evaluation indicators, the entropy weight-TOPSIS method is used to weight and aggregate the indicators for evaluation. The entropy weight method is adopted for objective weighting based on the data itself, avoiding subjective biases caused by artificial weighting. Static evaluation focuses on the inherent structural performance of networks, with the core objective of quantifying performance differences among various C2 structures. This requires an objective ranking of multiple metrics. The advantage of the TOPSIS method lies in its distance measurement based on ideal solutions versus negative ideal solutions, which clearly identifies the gap between each structure and optimal performance while avoiding subjective human bias [35]. The fully connected optimal collaborative structure of distributed networks and the minimal command structure of centralized networks inherently form the upper and lower bounds of C2 performance. This provides explicit references to ideal and negative-ideal solutions for TOPSIS, enhancing the tactical significance of static ranking. The method exhibits low sensitivity to multi-criteria weighting, aligning with the comprehensive ranking requirements of 10 evaluation metrics and ensuring the objectivity of static evaluation. The static evaluation algorithms for the drone swarm C2 network are as Algorithm 1.

Algorithm 1 Evaluation for Drone Swarm C2 Network Quality

Require: Evaluation scenarios Ensure: Static evaluation value $Q_{\mathrm{sta}}$   1: for each scenario ∈ Scenarios do   2:     Compute metric matrix $X=\left\{x_{ij}\right\}$ in Equation (10)   3:     Normalize X to $X^{\prime }=\left\{x_{ij}^{\prime }\right\}$ in Equations (11) and (12)   4: end for   5: Compute $p_{ij}$ from $x_{ij}^{\prime }$ in Equation (13)   6: Compute entropy $e_j$ in Equation (14)   7: Compute weights $w_j$ in Equation (15)   8: Construct weighted matrix $Z=X^{\prime }·\mathrm{diag}\left(W\right)$ in Equation (16)   9: Compute $D_i^{+},D_i^{-}$ in Equation (17) 10: Compute $Q_{\mathrm{sta}}\left(i\right)$ in Equation (18) 11: return $Q_{\mathrm{sta}}$ for all schemes

Step 1: Data preparation and standardization. Assume there are m schemes with n indicator values. Let $x_{ij}$ represent the value of the j indicator of the i scheme, the decision matrix is

$$X=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right]$$

(12)

Subsequently, the max-min normalisation method is used to normalise the data. The normalisation equations for positive indicators and negative indicators are shown in Equations (13) and (14), respectively. A value of 0.01 is added to prevent the normalised value from being 0, thus avoiding invalid values.

$$x_{ij}^{\prime }={\displaystyle \frac{x_{ij}-x_{i\min }}{x_{i\max }-x_{i\min }}}+0.01$$

(13)

$$x_{ij}^{\prime }={\displaystyle \frac{x_{i\max }-x_{ij}}{x_{i\max }-x_{i\min }}}+0.01$$

(14)

Step 2: Weight determination using the entropy weight method. First, calculate the proportion of the i scheme under the j indicator, as shown in Equation (15).

$$p_{ij}={\displaystyle \frac{x_{ij}^{\prime }}{{\sum }_{i=1}^m{x}_{ij}^{\prime }}}$$

(15)

Further, the entropy weight method is used to calculate the information entropy value, as expressed in Equation (16).

$$e_j=-{\displaystyle \frac{1}{lnn}}\sum _{i=1}^m{p}_{ij}ln\left(p_{ij}\right)\left(0\le e_j\le 1\right)$$

(16)

Based on the information entropy of each indicator, the weight value of each indicator is calculated, as shown in Equation (17).

$$w_j={\displaystyle \frac{1-e_j}{m-{\sum }_{j=1}^m{e}_j}}$$

(17)

Step 3: Construction of the weighted normalised matrix. The entropy weight vector composed of the weight values of each indicator is $W=(w_1,w_2,\dots ,w_m)$, the weighted normalised matrix is then constructed, as shown in Equation (18).

$$Z=X^{\prime }\times \mathrm{diag}\left(W\right)=\left[\begin{array}{cccc}{x}_{11}^{\prime }& x_{12}^{\prime }& \dots & x_{1n}^{\prime }\\ x_{21}^{\prime }& x_{22}^{\prime }& \dots & x_{2n}^{\prime }\\ ⋮& ⋮& \ddots & ⋮\\ x_{m1}^{\prime }& x_{m2}^{\prime }& \dots & x_{mn}^{\prime }\end{array}\right]\times \left[\begin{array}{cccc}{w}_1& 0& \dots & 0\\ 0& w_2& \dots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \dots & w_n\end{array}\right]=\left[\begin{array}{cccc}{z}_{11}& z_{12}& \dots & z_{1n}\\ z_{21}& z_{22}& \dots & z_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ z_{m1}& z_{m2}& \dots & z_{mn}\end{array}\right]$$

(18)

Step 4: Calculation of the distance between each scheme and the ideal solution. The positive ideal solution and negative ideal solution represent the schemes with the maximum and minimum indicator values, respectively. Calculate the Euclidean distance between the value of the i-th scheme and the positive ideal solution, as well as that between the value of the i-th scheme and the negative ideal solution, as shown in Equation (19).

$$\left\{\begin{array}{c}{D}_i^{+}=\sqrt{{\sum }_{j=1}^n{\left(x_j^{+}-w_j\times Z_{ij}\right)}^2}\hfill \\ D_i^{-}=\sqrt{{\sum }_{j=1}^n{\left(x_j^{-}-w_j\times Z_{ij}\right)}^2}\hfill \end{array}\right.$$

(19)

Step 5: Calculate the relative closeness of each scheme. The relative closeness comprehensively considers the degree to which a scheme is close to the positive ideal solution and far from the negative ideal solution, which is the network quality evaluation result, as shown in Equation (20).

$$Q_{\mathrm{sta}\left(i\right)}={\displaystyle \frac{D_i^{-}}{D_i^{+}-D_i^{-}}}$$

(20)

3.2.2. Dynamic Evaluation Method

Dynamic evaluation is conducted by simulating attacks on the network, calculating the network quality indicator values after each attack wave, and then comprehensively evaluating the network quality after the attack. By analyzing the stability of network quality evaluation values after each attack wave, it can provide a reference for measuring network robustness, thereby making the dynamic evaluation more comprehensive. Dynamic evaluation simulates network performance changes under random and deliberate attacks, focusing on the evolutionary stability of network performance in attack scenarios. The core requirement is to handle data uncertainty in the face of dynamic changes. The GRA method excels at analyzing correlations in dynamic sequences without strict requirements on data distribution. It effectively handles abrupt metric changes during attacks and quantifies the alignment between actual and ideal trends using grey relational analysis. Compared to TOPSIS, GRA does not require predefined ideal solutions, making it more suitable for network quality evaluation under unknown attack intensities. The dynamic evaluation algorithms for the drone swarm C2 network are as Algorithm 2.

Algorithm 2 Dynamic Evaluation for Drone Swarm C2 Network Quality

Require: Evaluation scenarios, Attack types = {Random, Malicious} Ensure: Comprehensive dynamic evaluation value $Q_{\mathrm{dyn}}$   1: for each attack type ∈ Attack types do   2:      for each scheme ∈ Evaluation schemes do   3:          for each wave ∈ attack type do   4:             Construct indicator matrix $A_i$ in Equation (19)   5:             Normalize $A_i$ to $A_i^{\prime }$ and compute $G=A_i^{\prime }·{W^{\prime }}^T$ in Equation (20)   6:          end for   7:       end for   8: end for   9: Construct evaluation matrix B from G over all waves in Equation (21) 10: Compute grey relational matrix D using $\xi =0.5$ in Equations (22) and (23) 11: Compute $Q_{\mathrm{dyn}}=D·H^T$ in Equation (24) 12: return $Q_{\mathrm{dyn}}$

First, calculate the network quality indicator values after each round of attacks. Assume there are s schemes with t indicators, the evaluation matrix is then constructed as Equation (21).

$$A_i=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \dots & a_{1t}\\ a_{21}& a_{22}& \dots & a_{2t}\\ ⋮& ⋮& \ddots & ⋮\\ a_{s1}& a_{s2}& \dots & a_{st}\end{array}\right]$$

(21)

Different from static evaluation, the weights in dynamic evaluation are assigned based on the variation values of each network indicator. Generally, indicators with larger variations in their measured values have higher weights; therefore, the entropy weight method is scientifically suitable for weighting. Through weighting and aggregation, the network quality value vector of each scheme under each round of attacks can be obtained, as shown in Equation (22). Where $A^{\prime }$ is the normalised matrix of A, and $W^{\prime }$ is the indicator weight vector. Theoretically, the components of vector G show a decreasing trend.

$$G=A^{\prime }\times W^{\prime T}$$

(22)

For a further comprehensive dynamic network quality evaluation of each scheme, assuming there are u schemes with v wave-based network quality values, the evaluation matrix is constructed as Equation (23).

$$B=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \dots & b_{1v}\\ b_{21}& b_{22}& \dots & b_{2v}\\ ⋮& ⋮& \ddots & ⋮\\ b_{u1}& b_{u2}& \dots & b_{uv}\end{array}\right]$$

(23)

Based on the entropy weight method, the weight vector H for the network quality of each wave is calculated, and the grey relational analysis (GRA) method is applied for aggregation. The core idea of GRA is to compute the degree of correlation between the overall dataset and an ideal trend. Since the network quality values for each wave are derived from model calculations, the data inherently contains certain deviations, and the comprehensive dynamic network quality value of a scheme focuses more on the overall quality of the data, which aligns well with the fundamental principle of GRA. Moreover, GRA has low requirements for data quality, making it suitable for this study [36]. Let the normalized matrix of B be $B^{\prime }$, and let $B_0^{\prime }=\left(b_{01}^{\prime },b_{02}^{\prime },\dots ,b_{0n}^{\prime }\right)$ serve as the reference attribute set (i.e., the reference standard set vector) for the GRA. Given $b_{0j}^{\prime }=max\left\{b_{1j}^{\prime },b_{2j}^{\prime },\dots ,b_{nj}^{\prime }\right\}$, the equation for calculating the relational degree between the j wave of the i scheme and $B_0^{\prime }$ is expressed as Equation (24).

$$d_{ij}={\displaystyle \frac{\underset{i}{min}\underset{j}{min}\left|b_{0j}^{\prime }-b_{ij}^{\prime }\right|+\xi \underset{i}{max}\underset{j}{max}\left|b_{0j}^{\prime }-b_{ij}^{\prime }\right|}{\left|b_{0j}^{\prime }-b_{ij}^{\prime }\right|+\xi \underset{i}{max}\underset{j}{max}\left|b_{0j}^{\prime }-b_{ij}^{\prime }\right|}}$$

(24)

$\xi$ is the resolution coefficient, which is used to enhance the differences between relational coefficients. It is generally appropriate to set $\xi =0.5$. The calculated relational matrix is as Equation (25).

$$D=\left[\begin{array}{cccc}{d}_{11}& d_{12}& \dots & d_{1n}\\ d_{21}& d_{22}& \dots & d_{2v}\\ ⋮& ⋮& \ddots & ⋮\\ d_{u1}& d_{u2}& \dots & d_{uv}\end{array}\right]$$

(25)

Finally, based on the entropy weight-grey evaluation model, the comprehensive dynamic network quality evaluation values for each scheme are calculated to determine the superiority or inferiority of each scheme, as shown in Equation (26).

$$Q_{\mathrm{dyn}}=D\times H^T$$

(26)

Static evaluation focuses on ranking the strengths and weaknesses of inherent structural properties, while dynamic evaluation emphasizes the stability and trendiness of scenario adaptability. TOPSIS and GRA are respectively better suited for their respective scenarios. Together, they complement each other to form a comprehensive evaluation system.

4. Case Verification and Analysis

4.1. Case Network Modeling

In this paper, we analyze centralized, distributed, and three types of hierarchical C2 networks with a scale of 70 drone nodes. These networks are constructed with 1 ground station node, 7 leader drone nodes, and 63 sub-drone nodes, ensuring consistent scale and node ratios across different network types. For the ER random network-based hierarchical C2 network, further research is required on the configuration of $p_{LL}$, $p_{LS}$, and $p_{SS}$. We employed heatmaps to analyze the impact of network quality variations with respect to node count and pLL, pLS, and pSS, as illustrated in Figure 4.

As shown in Figure 4a–c, $p_{SS}$ exerts the most significant impact on network quality. When its value increases from 0.1 to 1.0, the network quality value rises by 250–300%. $p_{LS}$ has the second-most impact, with a network quality increase of approximately 120–140% when its value rises from 0.1 to 1.0. $p_{LL}$ exhibits the weakest impact on network quality, with an increase of only 60–80% when its value rises from 0.1 to 1.0. As shown in Figure 4a, when the number of nodes exceeds 80, the rate of change in network quality value with respect to $p_{LL}$ decreases significantly, indicating that the experimental scale is reasonably set. Figure 4d analyzes the variation rates of network quality values with respect to $p_{LL}$, $p_{LS}$ and $p_{SS}$ for a fleet of 70 drones. The variation rate becomes negative when $p_{LL}$ exceeds 0.2, and it significantly decreases when $p_{LS}$ and $p_{SS}$ exceed 0.3 and 0.5, respectively. Therefore, $p_{LL}$, $p_{LS}$, and $p_{SS}$ are set to 0.2, 0.3, and 0.5, respectively.

Scenarios 1, 2, and 3 are hierarchical C2 networks based on the Leader–Follower architecture, BA scale-free network, and ER random network, respectively, as shown in Figure 5a, Figure 5b and Figure 5c, respectively. Scenarios 4 and 5 are the centralized C2 network and distributed C2 network, respectively, constructed with 1 ground station node and 70 drone nodes, as shown in Figure 5d and Figure 5e, respectively.

4.2. Static Evaluation

Based on the calculation method of network quality evaluation indicators described in Section 3.1, the indicator values of the five case networks are obtained, as shown in

Table 1. Indicator values of case networks.

Indicator	Type	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
K	+	7.5600	5.8600	8.9859	1.9700	69.0000
C	+	0.9353	0.2214	0.1774	0	1
$\rho$	+	0.1890	0.0837	0.1284	0.0282	1
G	−	0.0771	0.3697	0.2276	0.4859	0
R	+	0.1220	0.0143	0.0282	0.0141	1
$\tau$	+	0.1031	−0.2872	−0.0971	−1.0000	1
E	+	0.4949	0.4667	0.5090	0.5141	1
T	+	15.3616	9.9129	13.0874	0.1786	28.4682
L	−	26.9000	29.6122	29.5434	29.1500	26.5000
T	−	1	1.6290	1.7526	1	1.0395

The symbols ‘+’ and ‘−’ in the table indicate whether the corresponding indicator is a positive or negative indicator.

.

The results of indicator normalisation are shown in

Table 2. Indicator normalization results.

Indicator	Type	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
K	+	0.0934	0.0680	0.1147	0.01	1.01
C	+	0.9453	0.2314	0.1874	0.01	1.01
$\rho$	+	0.1755	0.0671	0.1131	0.01	1.01
G	−	0.8513	0.2491	0.5416	0.01	1.01
R	+	0.1194	0.0102	0.0243	0.01	1.01
$\tau$	+	0.5616	0.3664	0.4616	0.01	1.01
E	+	0.0629	0.01	0.0893	0.0989	1.01
T	+	0.5467	0.3541	0.4663	0.01	1.01
L	−	0.9004	0.1573	0.1762	0.01	1.01
T	−	1.01	0.8386	0.01	1.01	0.9575

The symbols ‘+’ and ‘−’ in the table indicate whether the corresponding indicator is a positive or negative indicator.

.

According to the static evaluation method described in Section 3.2.1, the network quality values of the schemes are evaluated. The indicator weights are 0.1536, 0.0806, 0.1372, 0.0583, 0.2037, 0.0525, 0.1604, and 0.1537, respectively. The TOPSIS method is used to conduct a comprehensive evaluation of the network quality values of each scheme; the evaluation results are shown in Figure 6a. The results indicate that the centralized network has the lowest quality value, which is consistent with the actual situation, verifying the effectiveness of the evaluation method. The results of the entropy-weighted GRA method and the multiple correlation coefficient method [21,22] are shown in Figure 6b,c. Comparison reveals that the entropy-weighted GRA method exhibits poor result differentiation, while the multiple correlation coefficient method yields outcomes inconsistent with reality. A limitation of the multiple correlation coefficient method is its exclusive focus on indicator relationships, which overlooks the actual contribution of indicators to C2 system’s core functions. This may result in the loss of weights for relatively independent indicators that significantly impact network quality, leading to distorted evaluation outcomes. Furthermore, existing methods generally lack deep adaptation to diverse drone swarm scenarios. The proposed evaluation framework not only overcomes these limitations but also employs multiple assessment models to distinguish scenario-specific evaluation characteristics and requirements. Static evaluation emphasizes “ranking the inherent performance advantages and disadvantages of structures,” while dynamic evaluation focuses on “the stability and trendiness of scenario adaptation capabilities.” Consequently, TOPSIS and GRA are respectively more suitable for their respective scenarios. The GRA method’s lower accuracy in static evaluation compared to the TOPSIS method supports the rationality of the proposed evaluation framework.

Based on the evaluation results of the three hierarchical C2 networks, it can be concluded that the hierarchical network built on the leader–follower framework demonstrates superior stability and is better suited for missions characterized by long endurance and low confrontation. Given that sufficient existing research has verified the advantages and disadvantages of centralized and distributed C2 structures, subsequent analysis will be focused solely on the quality of the three hierarchical C2 networks.

4.3. Dynamic Evaluation

Dynamic evaluation mainly focuses on the three hierarchical C2 networks mentioned above (based on the Leader–Follower architecture, BA scale-free network, and ER random network), further evaluating the network quality of the three C2 structures when facing attacks. The prerequisite for studying network dynamic evaluation is to analyze and model its dynamic evolution process, and this paper conducts the research by taking node attacks as an example. Analyses are conducted from two perspectives: random attacks and targeted attacks. A total of 20 rounds of random attacks are simulated, with 1 node attacked in each round, and all types of nodes have the same probability of being attacked. Seven rounds of targeted attacks are simulated, focusing on attacking leader drone nodes. For three types of C2 networks subjected to random and targeted attacks, 100 Monte Carlo simulations were conducted, with results averaged. Each simulation independently generated an attack sequence, ensuring all nodes faced an equal probability of being attacked.

4.3.1. Evaluation Results of Random Attacks

Twenty random attacks are conducted on the three hierarchical C2 networks (based on the Leader–Follower architecture, BA network, and ER network), and the network quality indicator evaluation values after each round are obtained. The indicator changes of the three structure networks under random attacks are shown in Figure 7, Figure 8 and Figure 9.

As observed from the Figure 7, Figure 8 and Figure 9, among the three structure networks, positive indicators such as average node degree K, network density $\rho$, network efficiency E, and link-to-node ratio $\lambda$ show a decreasing trend, while the negative indicator (load Gini coefficient) shows an increasing trend. This indicates that most indicators can correctly reflect changes in the network structure. Next, we will analyze the anomaly trend indicators for each scenario. In the Leader–Follower-based hierarchical network, the average clustering coefficient C shows a phased increasing trend, which is because the removal of an entire subnet (when a leader node fails) increases the overall clustering coefficient of the network. The increase in the node assortativity coefficient $\tau$ indicates that the network may split into multiple connected components as the attack proceeds, and the nodes within each connected component have similar degrees. In the BA scale-free network and the ER random network-based hierarchical network, the proportion of social nodes shows an upward trend, punctuated by abrupt changes. This occurs because in both network types, the command station node holds the highest degree value. As sub-drone nodes are attacked, the proportion of social nodes gradually increases. The abrupt change in the curve occurs when the leader drone nodes connected to the command station node are attacked, causing the network to develop nodes with the same degree as the command station node. After these nodes are attacked or their degree decreases, the curve resumes its original trend.

After obtaining the indicator value data for 20 waves, the entropy weight method is applied for weighted aggregation to derive the network quality evaluation values for each wave, as shown in Figure 10. By comparing changes in these network quality values, the network’s robustness can be analyzed.

The figure clearly shows that the network quality of the Leader–Follower-based hierarchical C2 network exhibits a small fluctuation range, indicating that this structure is more robust than the other two. Using the dynamic evaluation method described in Section 3.2.2, the comprehensive dynamic network quality evaluation values are obtained, as shown in Figure 11. The conclusion is drawn that under random attack scenarios, the performance follows the order: Scenario 1 > Scenario 3 > Scenario 2.

Boxplots are used for further quantitative analysis of the stability of the network quality values of the three scenarios under rounds of attacks, as shown in Figure 12. The average network quality values of the three scenarios are 0.4783, 0.4229, and 0.4415, respectively, and the standard deviations are 0.0633, 0.0886, and 0.0465, respectively. It can be clearly observed that Scenario 1 is superior to Scenario 3, which is superior to Scenario 2. The network quality of the Leader–Follower-based distributed C2 structure is significantly more stable than that of the other two structures.

4.3.2. Evaluation Results of Targeted Attacks

As the hub node of the hierarchical C2 network, the failure of a leader node exposes control stations and sub-drones to the risk of disconnection. Therefore, targeted attacks mainly focus on attacking the 7 leader drone nodes sequentially. After obtaining the network quality evaluation indicator values of 7 rounds, weighting and aggregation are conducted using the dynamic evaluation method, resulting in the network quality evaluation values of each round, as shown in Figure 13.

Using the dynamic evaluation method, the comprehensive dynamic network quality evaluation values are obtained, as shown in Figure 14. It can be concluded that under targeted attack scenarios, the network quality comprehensive evaluation values follow the order: Scenario 3 > Scenario 2 > Scenario 1. This indicates that the Leader–Follower-based hierarchical C2 network has a high dependence on leader nodes; therefore, attention should be paid to the protection of leader nodes and the improvement of their anti-destruction capabilities.

In summary, the network quality evaluation results for three types of hierarchical C2 networks under different conditions are shown in

Table 3. Comparison of evaluation results for three types of hierarchical C2 networks.

	Scenario 1	Scenario 2	Scenario 3
Static evaluation	0.4350	0.2248	0.2405
Random attacks	0.8311	0.3815	0.6640
Targeted attacks	0.4473	0.6382	0.7445

.

In summary, the Leader–Follower-based network exhibits good performance in terms of static structure and under random attacks, but has the worst performance under targeted attacks. This reflects the high dependence of its network structure on leader nodes, making it suitable for long-endurance, long-range tasks such as vigilance patrols and reconnaissance and surveillance, or large-scale deployment scenarios, but not for operational tasks with strong confrontation. Its tactical advantages lie in a clear command chain and load balancing, ensuring continuous command transmission during prolonged missions. This aligns with the core requirements of reconnaissance tasks: low latency and high stability. Although the BA network and ER network have relatively poor performance in terms of static structure and under random attacks, they perform better under targeted attacks. In particular, the hierarchical C2 network based on ER random networks exhibits optimal survivability against deliberate attacks, making it more suitable for high-intensity, fast-paced adversarial operations (such as precision strikes and swarm penetration). Its strong connection, randomness, and absence of distinct core nodes provide effective resistance against targeted attacks on leader nodes, ensuring operational continuity.

5. Conclusions

This study proposes a quality evaluation method for drone swarm C2 networks based on complex networks, evaluating the structure of the drone swarm C2 system from the perspective of topological structure. The feasibility and effectiveness of the method are verified through case analysis, and the main conclusions are as follows:

• Complex networks can accurately characterise the structure of the drone swarm C2 system. By modeling the drone swarm C2 system as a network, complex network theory can be used to effectively analyse it.
• The network quality evaluation indicator system comprehensively considers three aspects: network connectivity, network load status, and network transmission efficiency. The method considers both static and dynamic characteristics, and the evaluation framework provides a reference for analyzing and evaluating other operational systems.
• The case analysis results indicate that hierarchical C2 networks with different structures have their own advantages and disadvantages under different scenarios (static conditions, random attacks, and targeted attacks). The effectiveness of the method is verified by comparing distributed and centralized networks. The dynamic network evaluation further demonstrates the universality of the evaluation method across networks with different structures, enabling it to guide the design of C2 system architectures.

This study focuses on the network quality of the C2 system from a network modeling and analysis perspective. The following areas can be further deepened to better align with practical scenarios and technological development needs.

• Current research focuses on single-function drone swarm C2 networks, whereas actual combat operations often involve the coordination of heterogeneous drones performing diverse tasks such as reconnaissance, strike, and communication relay. Future work should leverage the functional differences among heterogeneous nodes and integrate task performance metrics to build a hybrid evaluation framework that combines structural characteristics with actual task outcomes, making the evaluation results more directly serve the optimization of UAV swarm C2 system design for specific tasks.
• Current evaluations rely on predefined metric systems and optimization algorithms, lacking adaptability to unknown scenarios. Future approaches should incorporate machine learning or deep learning methods to enable models to autonomously learn optimal structural characteristics of C2 networks across diverse battlefield conditions. This would establish an integrated “evaluation–decision” intelligent framework, enhancing the drone swarm C2 system’s dynamic adjustment and autonomous operational capabilities.
• Current research on the drone swarm C2 network remains primarily focused on theoretical modeling and simulation analysis, with physical verification facing multiple practical obstacles. This paper primarily provides theoretical support at the modeling and simulation level for the advantages, disadvantages, and mission adaptability of swarm systems employing different command and control methods, though it lacks sufficient practical validation. Subsequent work will involve the development and utilization of a semi-physical simulation platform for drone swarms to collect real communication data and control response logs for verifying the experimental results presented herein. By comparing the measured data with the simulation results of the proposed evaluation model, we will verify the accuracy and practical applicability of the model, and gradually promote the transformation from theoretical simulation to engineering application-oriented validation.