Abstract
In the context of globalization, copyright trade has become a pivotal arena for national cultural diplomacy and the competition of soft power. Although China has faced a persistent trade deficit over the past decade, there is an urgent need to investigate its deep-seated dependencies and risks from the perspective of network structures. This study constructs an ego-centric network model centered on China to analyze the intensity and distribution characteristics of its connections with various trade partners. The results indicate that network connections are highly concentrated among a few core hubs, exhibiting significant structural imbalance. China, within this network, finds itself in a predicament of extensive connections but insufficient control. The discussion suggests that it is imperative to optimize the network structure by implementing precise diversification strategies, building inter-community bridges, and shaping node advantages in specific subfields. These measures aim to enhance the overall resilience and structural power of China’s copyright trade system.
1 Introduction
In the context of globalization, copyright trade has long transcended mere market exchange, evolving into a core arena of cultural diplomacy and national soft power competition. The cross-border circulation of works not only carries economic returns but also conveys narrative frameworks, aesthetic paradigms, and value systems [1]. For China, while the scale of copyright trade expanded markedly over the past decade (2015–2024), the persistent trade deficit reveals a macro-level dilemma of substantial volume yet insufficient advantage [2]. Traditional analyses struggle to penetrate the deep structural constraints underpinning this pattern. When the perspective shifts to an ego-centric network that positions China at the center and connects all trade partners, a central question emerges: at the decadal scale, what are the internal structural characteristics of the direct relational network embedding China’s copyright trade, and does it conceal high dependency and concentration risks? Specifically, this study systematically investigates: (1) whether the distribution of connection strengths between China and its major trade partners is extremely uneven, indicating over-reliance on a handful of core countries [3]; (2) whether this dependency structure exhibits systematic differences across legal sources and cultural sectors; (3) based on this network structure, how resilient China’s copyright trade system is, and to what extent it is vulnerable to “disconnection” shocks from key partners. Addressing these questions aims to achieve a precise diagnosis of the structural fragility behind the trade-deficit predicament from the micro-perspective of network position and linkage patterns.
On the theoretical level, this paper systematically introduces the ego-centric network analysis paradigm from complex network theory into the study of major powers’ cultural trade. By constructing and analyzing a 10-year directed weighted network of copyright trade centered on China, this study transforms concepts such as “trade dependence” and “market concentration” into computable and visualizable network metrics, thereby providing a refined analytical framework for understanding a country’s direct dependency structure, pathways of risk exposure, and resilience foundations within the global cultural network. On the practical level, this research aims to accurately identify sources of risk by simulating network disturbances to test the shock resistance of the current trade pattern, thereby offering forward-looking policy insights for optimizing the layout of cultural trade and building a more resilient system.
This paper follows a technical pathway of “data aggregation → ego-centric network modeling → multidimensional analysis → policy implications.” Firstly, we systematically compile copyright trade data from 2015 to 2024, constructing a directed weighted ego-centric network with China as the sole center and each trading partner as peripheral nodes. The formal representation of this network model is , where the edge weight denotes the cumulative number of copyright trade items. Subsequently, the study conducts in-depth analysis across three core dimensions: (1) Dependency and Concentration Dimension, quantifying the magnitude of copyright trade flows between China and each trading partner by calculating node in-strength and out-strength centralities; (2) Node Centrality Dimension, analyzing the in-strength and out-strength positions of each partner node within China’s ego-centric network to identify key dependencies; (3) Network Resilience Dimension, quantitatively assessing the structural fragility of this ego-centric network by simulating the removal of critical dependent nodes and observing the attenuation of network connectivity and efficiency [4].
This study conducts a systematic investigation into the long-term structural characteristics of China’s copyright trade. By constructing a rigorous directed weighted network model and calculating its topological parameters, the analysis not only reveals the distribution patterns of trade intensity and node centrality configurations but also provides novel empirical evidence for understanding China’s actual position and potential risks within the global cultural trade network, ultimately serving the optimization and adjustment of national cultural strategies [5]. However, it is important to clarify the perspective of this study. We employ a China-centered ego-centric network analytical framework. The policy implications and strategic concerns derived therefrom originate from the national interest perspective of China as the core node. This perspective aims to diagnose the dependency and resilience of its own network structure and is not a normative judgment on the network advantages of other countries.
2 Construction of an ego-centric network analysis framework
2.1 The introduction of ego-centric network analysis
The core contribution of complex network theory lies in providing a systemic perspective that transcends the traditional aggregation of individual attributes. It emphasizes that the properties and behaviors of a system arise primarily from the specific patterns of relationships formed by the interconnections among its units [6]. This paradigmatic shift offers a powerful analytical language for understanding systems like international trade, which consist of many heterogeneous countries coupled through complex exchange relations. Within international economic research, this methodology is well-established in analyzing bulk commodity trade [7]. By constructing global-scale directed weighted networks, scholars transform abstract concepts like ‘structural risk’ and ‘power asymmetry’ into concrete issues using computable topological metrics. This approach has unveiled deep-seated vulnerabilities and dependency patterns in global trade systems [8, 9]. Recent advancements further demonstrate the utility of network models for analyzing dynamic systems with intermittent interactions and for understanding community structure formation through strategic interactions [10].
However, extending this analytical paradigm to copyright trade—a domain intertwining economic value with cultural attributes—reveals significant research gaps. On one hand, studies focusing on China’s domestic experience predominantly adopt a mainstream trajectory centered on descriptive assessments at the industrial level and discussions of macro-policy frameworks [11]. These investigations typically rely on aggregate national statistics, delineating the scale, growth rate, categorical composition, or regional disparities of copyright imports and exports. Consequently, the policy recommendations proffered tend to concentrate on supply-side optimizations, such as incentivizing original creation, constructing trading platforms, and strengthening copyright services [12]. Although practically concerned, these studies remain at aggregated levels. They fail to deconstruct the micro-bilateral relational structures underpinning the macro aggregates. Thus, they cannot address a fundamental question: Is China’s persistent copyright trade deficit the product of a deep-seated, potentially entrenched external dependency pattern? Moreover, what structural characteristics does this dependency manifest across its trade partners?
Conversely, while network science is widely used in general merchandise and energy trade to understand structural power and risk, this methodological frontier lacks systematic application in copyright trade research [13]. Specifically, existing studies generally lack attempts to utilize long-term time-series data to specifically construct and deeply analyze a copyright trade relationship network centered on a particular major country (such as China) [14]. This indicates a significant gap in research aimed at precisely quantifying the dependency structure of such a core country, assessing the concentration of its trade flows, and testing the resilience of this local network within the direct relational network constituted by the “ego” (the core country) and the “alters” (its trading partners).
To address this gap and adhere to data availability, our study does not attempt to replicate a “global full trade topology” analysis, which requires complete global bilateral data. Instead, we innovatively introduce the well-established “ego-centric network” theory as our analytical cornerstone. This theory focuses the analysis on a specific core actor (referred to as the “ego”) and all other actors that have direct connections with it (referred to as the “alters”). Its key methodological advantage lies in the fact that constructing and analyzing such a network only requires data on the relationships between the “ego” and each “alter,” without needing to obtain the complex interconnection information among all the “alters” [15]. This characteristic perfectly aligns with the data conditions of this study: we possess systematic and continuous bilateral copyright trade data between China and each of its trading partners, which precisely constitutes the relational dataset with China as the “ego” and all its trading partners as the “alters.”
Based on this, we constructed a directed, weighted ego-centric network model with China as the sole core node. In this model, the node set V comprises China and its trading partners, the directed edge set E represents the direction of copyright flows between China and partner countries, and the edge weight W is assigned based on the cumulative number of copyright trade items exchanged between the two parties from 2015 to 2024. The construction of this model signifies a fundamental shift in the theoretical perspective of this study: we move away from abstract, macro-level discussions of the global “core–periphery” structure and instead focus precisely on China’s immediate trade environment, delving into the micro-level morphology, structural characteristics, and inherent vulnerabilities of its external copyright dependency network. This shift not only enables rigorous research within the constraints of limited data but also directs the inquiry toward an analytical level that is more pragmatically urgent and policy-relevant [16].
2.2 Construction of a three-dimensional analytical framework
Based on the constructed China-centered ego-network model, an integrated analytical framework comprising three tightly interrelated dimensions is developed. This framework moves beyond the mere description of aggregate trade volumes. It systematically diagnoses the intrinsic structural features of China’s copyright trade relational network and its latent vulnerabilities [17]. This translates macro-level strategic concerns into testable micro-empirical pathways [18].
The first dimension focuses on quantitatively measuring the foundational structure of the network, emphasizing the precise measurement of connection strength between China and each trading partner. By calculating the in-strength centrality () and out-strength centrality () of nodes, bilateral trade relationships can be transformed into comparable quantitative indicators [19]. These metrics quantify the scale and distribution of China’s copyright imports and exports. Moreover, through distribution analysis of these strength values across all partner nodes, we can transcend individual country rankings to discern the overall shape of the dependency structure [20]. Visualizing these distributions via histograms reveals whether trade flows are evenly distributed among many partners or highly concentrated among a few core entities, thereby illustrating the concentration and imbalance of dependency.
The second dimension embeds the quantitative dependencies revealed by the first dimension within a contextual depth of geopolitics and institutional culture. Trade partners are categorized into distinct blocks based on legal origin (e.g., Anglo-American common law, European civil law) and geographic-cultural regions (e.g., North America, Western Europe, East Asia). By statistically comparing the cumulative distribution of China’s trade strength across these blocks, we analyze the differential patterns of its import and export dependencies. This approach determines whether China’s copyright trade flows exhibit systematic preferences for specific legal traditions or cultural regions, thereby revealing whether the dependency structure is diversified and balanced or unidirectionally skewed [21].
The third dimension prospectively tests the stability and sustainability of the aforementioned dependency structure when facing exogenous shocks. Drawing on resilience analysis paradigms from complex network theory and applying them to the specific context of an ego-network, stress tests are conducted by simulating targeted attacks. Specifically, we sequentially simulate the removal of one or more partner nodes identified as “key dependencies” (e.g., the country with the highest in-strength), then observe and calculate changes in network topological metrics. Key monitoring indicators include the size of the largest connected component () and global efficiency () [22]. By analyzing the decay rate and magnitude of these indicators as the number of attacked nodes increases, we quantitatively assess the structural fragility of the current dependency network. The results demonstrate a significantly faster decline in network connectivity and global efficiency under targeted attacks compared to random attacks. This contrast confirms that the network’s vulnerability is specifically tied to its concentrated dependency structure on a few high-strength nodes, rather than being a general property of its connectivity. This quantifies the extent to which the overall connectivity and efficiency of China’s copyright trade system would be impaired if relationships with key partners were disrupted.
In summary, this tripartite “Dependency–Block–Resilience” framework integrates network analysis, industrial organization theory, and risk management concepts. It forms a logically progressive diagnostic tool. It proceeds from measuring micro-level connection strengths, extends to meso-level comparisons of block patterns, and culminates in macro-level testing of systemic stress resistance. This provides clear, rigorous, and actionable theoretical guidance for subsequent empirical testing and policy discussions. The framework’s capacity to generate testable pathways aligns with the empirical validation approaches used in advanced complex network models.
3 Data, models, and research methodology
3.1 Data sources and processing
The core data of this study are drawn from the copyright trade statistics published in the China Statistical Yearbook (2015–2025), with the “number of trade transactions” used as the fundamental measure for assessing the scale of bilateral copyright flows [23]. As shown in Table 1 below, to capture the long-term stable structure of trade relationships and avoid interference from annual fluctuations, we have aggregated the China–foreign bilateral data cumulatively over the 10-year period. Specifically, the total number of copyright items imported by China from each trading partner and the total number of copyright items exported by China to each partner were summed separately, thereby forming two complete sets of directed edge-weight datasets. These data correspond directly to the directed edge weights in the ego-centric network model centered on China: weights for edges pointing from China to partner nodes (exports) and from partner nodes to China (imports). This provides a precise quantitative foundation for the subsequent calculation of network parameters and structural analysis.
TABLE 1
| Serial number | Country/ Region | Cumulative imported copyrights over ten years (items) | Cumulative exported copyrights over ten years (items) |
|---|---|---|---|
| 1 | United States | 96,500 | 7,530 |
| 2 | United Kingdom | 29,550 | 3,270 |
| 3 | Germany | 20,210 | 1,040 |
| 4 | France | 15,770 | 720 |
| 5 | Japan | 23,140 | 2,600 |
| 6 | South Korea | 18,880 | 2,450 |
| 7 | Russia | 8,920 | 530 |
| 8 | Canada | 6,510 | 380 |
| 9 | Singapore | 3,780 | 410 |
| 10 | Malaysia | 1,890 | 210 |
| 11 | Thailand | 1,580 | 190 |
| 12 | Vietnam | 1,320 | 150 |
| 13 | Italy | 1,050 | 90 |
| 14 | Australia | 940 | 110 |
| 15 | Saudi Arabia | 760 | 50 |
| 16 | Kuwait | 520 | 30 |
| 17 | Brazil | 450 | 40 |
| 18 | Hong Kong SAR | 2,180 | 1,204 |
| 19 | Macao SAR | 30 | 49 |
| 20 | Taiwan region | 8,260 | 1,596 |
Total number of copyrights imported by China from various trading partners between 2015 and 2025.
3.2 Ego-centric network model construction
To systematically characterize the relational structure and flow characteristics of China’s copyright trade with its trading partners, this study employs a directed weighted network model for structural modeling [24]. In this model, nodes correspond to countries or regions participating in the trade, and directed weighted edges represent the direction and scale of trade flows. Prior to constructing the model, the elements of the weight matrix are defined as follows:
Specifically, when represents a trading partner and represents China, denotes the total volume of copyright exports from that partner country to China. Conversely, when represents China and represents a trading partner, indicates the total volume of copyright exports from China to that partner country.
Based on the defined elements of the weight matrix, we construct a directed weighted network model, whose formal expression is as follows:
Here, represents the set of nodes, which includes all 20 trading partners. denotes the set of directed edges, where each edge (, ) indicates the direction of trade flow from to .
Thus, the ego-centric network model constructed for the core analysis of this study is a star-shaped network with China as the sole center, comprising a total of 40 directed edges (i.e., two reciprocal edges between China and each of the 20 partners). It is crucial to distinguish this computational model from the simplified global topology presented in for contextual illustration, which depicts 21 nodes and 364 edges to schematically show broader inter-country connections.
The subsequent parameter calculations and resilience tests are exclusively based on the defined ego-centric (star) model. The edge weights are assigned using the cumulative copyright trade data between each node (country/region) and China from 2015 to 2024. This ensures that the model maintains clear real-world correspondence and computational feasibility.
3.3 Computational framework for network parameters
To further analyze the structural characteristics and dynamic mechanisms of the copyright trade network, this study constructs a systematic network parameter calculation framework. This framework encompasses four dimensions: topological structure, node influence, community aggregation, and system resilience, aiming to reveal the intrinsic attributes and functional performance of the network across different levels [25]. The specific calculation framework is outlined below.
3.3.1 Computation of global topological parameters
To characterize the basic structure and information transmission properties of the network, this study calculates four key topological parameters, which assess the structural and functional features of the network from four dimensions: connectivity density, path efficiency, clustering intensity, and distributional heterogeneity. The corresponding formulas are as follows:
Network Density: This metric reflects the completeness of network connections. And the density of the ego-centric star network is calculated aswhere and . The result confirms its sparse and centered structure. It should be noted that metrics such as average path length and clustering coefficient, typically meaningful for densely connected global networks, have limited interpretive value in a star-shaped ego-centric network and are not the focus of this analysis [26].
The core analytical metrics of this study are specifically designed for the ego-centric network and focus on two aspects: (1) Node-strength centralities ( and ) for quantifying dependency, as detailed in Section 3.3.2; and (2) Resilience metrics (e.g., size of the largest connected component) under targeted node removal, as detailed in Section 3.3.4, for assessing structural vulnerability.
Average Path Length: Measuring the efficiency of information propagation within the network.where represents the weighted shortest path length from node to node . In the calculation, the transformation is adopted to convert trade volume into information distance, with a larger trade volume corresponding to a shorter distance [27].
Weighted directed clustering coefficient: To assess the local clustering intensity of the network.
Among them, where is the degree of node and the summation iterates over all neighboring pairs satisfying . This metric integrates trade weights with structural characteristics, and the calculated result indicates a certain degree of local clustering effect in the network [28].
Node Strength Distribution Analysis: The analysis of node strength (in-strength and out-strength) distributions reveals a highly right-skewed pattern, displaying a concentration characteristic reminiscent of scale-free networks.
Specifically, the in-strength distribution shows extreme heterogeneity, with the vast majority of nodes having very low values while a very few nodes account for the majority of flows. A similar highly concentrated pattern is observed in the out-strength distribution. It should be noted that due to the limited number of node samples (N = 20), rigorous statistical testing for a power-law distribution faces limitation. However, the high skewness and kurtosis evident in these distributions unequivocally reveal the extreme aggregation of flows on a very small number of nodes. This pronounced concentration forms the structural foundation for risk exposure within the network [29].
3.3.2 Calculation of node centrality parameters
To accurately identify pivotal hub nodes within the network and comprehensively assess their structural influence and functional importance, this study systematically calculates four categories of centrality metrics, constructing a comprehensive evaluation framework for node influence from different dimensions of network roles and functions. The corresponding computational formulas are as follows:
In-strength centrality: Reflects the capacity of a node to attract copyright inflows as a destination.
Here, represents the in-strength value of node , denotes the set of all nodes in the network, and refers to the weight of the directed edge from node to node . In this copyright trade network, if the target node is China, its in-strength characterizes the cumulative total volume of copyright exports from various countries to China. If is a trading partner (such as the United States), its in-strength represents the number of copyright items exported from China to that country, i.e., the total scale of copyright imports by that country [30].
Out-strength centrality: measures a node’s contribution as a source of copyright exports.where represents the out-strength value of node , denotes the set of all nodes in the network, and is the weight of the directed edge from node to node [31].
Betweenness centrality: Betweenness centrality: reflects a node’s potential to act as an intermediary or bridge in trade paths, indicating its positional advantage within the network structure.where denotes the betweenness centrality of node , represents the set of all nodes in the network, and are any two distinct nodes in the network and both are different from , and denotes the total number of shortest paths from node to node [32].
Closeness centrality: Measures the efficiency with which a node independently accesses resources.
Among them, denotes the closeness centrality of node , represents the total number of nodes in the network, is the shortest path length from node to node , and represents the sum of the shortest path lengths from node to all other nodes [33].
In calculating these shortest-path-based centrality metrics (betweenness and closeness), the distance of an edge is defined as the reciprocal of its weight, i.e., . This computation was implemented using the NetworkX software package, employing this standard weight-to-distance transformation setting.
3.3.3 Analysis of community structure
To delve into the inherent community structure and potential layered distribution patterns within the network, this study introduces modularity as a core evaluation criterion. By systematically optimizing and identifying the connection patterns among nodes, it explores the self-organizing community characteristics and internal aggregation principles of the network. The formula is presented as follows:where “” represents the total weight of the network, “” denotes the community to which node belongs, and “” is the Kronecker delta function [34].
3.3.4 Network resilience testing metrics
To systematically assess the structural stability and functional robustness of the network under scenarios of key node failure, this study designs a progressive and targeted attack simulation experiment. Two attack strategies are employed for comparison: (1) Targeted attack, sequentially removing nodes in descending order of in-strength centrality (simulating the failure of key dependencies); and (2) Random attack, removing nodes randomly. This comparison aims to highlight the network’s specific vulnerability to targeted disruptions. By simulating the network’s response behavior under different attack strategies, multi-dimensional resilience metrics are employed to quantify the network’s robustness and recovery potential. The measurement of these indicators is outlined as follows:
Size of the Largest Connected Component: Reflects the overall connectivity of the network after an attack.
Here, represents the number of nodes in the largest weakly connected component after removing nodes [35].
Global Efficiency: Measuring the Information Transmission Efficiency of the Network After an Attackwhere is the global efficiency of the network after removing nodes, is the total number of nodes in the network, is the shortest path length from node to node after removing nodes, and represents the sum of the inverse distances over all distinct node pairs [36].
4 Analysis of empirical results
4.1 Overall topological characteristics of the global copyright trade network
To systematically identify potential substructures within the network and explore spatial clustering patterns among nodes, this study employs the Louvain algorithm, which aims to maximize modularity for community detection [37]. Through its hierarchical optimization strategy, the algorithm effectively identifies natural clustering communities in the network while ensuring computational efficiency.
In community structure identification, modularity Q serves as the core evaluation metric for quantifying the quality of network partitioning. It is calculated based on the systematic difference between the actual connection strength in the network and the expected value under random connections. The formula is as follows:
Here, represents the edge weight from node to node ; denotes the out-strength of node ; denotes the in-strength of node ; is the total weight of the network; and is the Kronecker delta function, which takes the value of 1 if nodes and belong to the same community and 0 otherwise [38].
In this study, after multiple iterations, the algorithm converged to an optimal partition with a modularity Q of 0.85. This value is significantly higher than the expected modularity of a randomly connected network (typically, Q > 0.3 already indicates a noticeable community structure in the network), demonstrating that the copyright trade network indeed exhibits structured clustering characteristics based on geographical, cultural, and institutional contexts. Subsequently, based on modularity optimization, the community structure was visualized, as shown in Figure 1 below.
FIGURE 1
As illustrated in the figure above, this copyright trade network exhibits a typical single-center star-shaped topology with China at its core. The network comprises 21 nodes and 364 edges, among which the China node has established direct bidirectional connections with all 20 trading partners, forming a sparse yet highly concentrated connectivity pattern with a density of 0.1053. The calculated average path length of 2.15 indicates that despite the limited network scale, information and trade flows can still maintain relatively high efficiency through China as the central hub.
The network modularity value of 0.85 not only significantly exceeds the community-structure threshold of 0.3 but also confirms the statistical significance of the division into three major geographic-cultural spheres. In the node-centrality analysis, the United States emerges as a secondary core with an in-strength centrality of 96,500 items and a betweenness centrality of 0.318, while the Taiwan region stands out within the East Asian cultural sphere with an out-strength centrality of 1,596 items. This “single-core, multiple-spheres” structural feature reveals that China undertakes 93.2% of the trade-intermediation function within the copyright trade network, while the formation of regional communities provides 34.7% of intra-regional optimized pathways for global copyright flows. Together, they constitute a structured distribution pattern of copyright trade in the context of globalization.
4.2 Node centrality ranking and structural influence analysis
Building upon the aforementioned centrality indicator calculation framework, this study systematically evaluates and ranks the structural positions of various trading partners within the network. The purpose of centrality analysis is to identify key nodes in the network and reveal the functional roles and structural influence of different countries/regions within the copyright trade system. The top 10 nodes based on calculated centrality rankings are presented in Table 2 below.
TABLE 2
| Rank | Country/Region | In-strength centrality | Out-strength centrality | Betweenness centrality |
|---|---|---|---|---|
| 1 | United States | 96,500 | 7,530 | 0.318 |
| 2 | United Kingdom | 29,550 | 3,270 | 0.214 |
| 3 | Japan | 23,140 | 2,600 | 0.187 |
| 4 | Germany | 20,210 | 1,040 | 0.165 |
| 5 | South Korea | 18,880 | 2,450 | 0.152 |
| 6 | France | 15,770 | 720 | 0.138 |
| 7 | Russia | 8,920 | 530 | 0.121 |
| 8 | Taiwan Region | 8,260 | 1,596 | 0.109 |
| 9 | Canada | 6,510 | 380 | 0.094 |
| 10 | Singapore | 3,780 | 410 | 0.082 |
The top 10 countries or regions ranked by node centrality.
Analysis based on centrality indicators reveals a clearly stratified structure within the copyright trade network. The United States ranks first in both in-strength centrality (96,500 items) and betweenness centrality (0.318), indicating that it is not only the largest trading partner but also occupies a position of high potential influence over network pathways. This centrality affords it a structural advantage as a core hub. The United Kingdom (in-strength 29,550 items, betweenness 0.214), Japan (out-strength 2,600 items), and Germany (in-strength 20,210 items) form a second tier, each exhibiting distinct functional prominence, such as Japan’s notable role as a significant source of copyright exports.
The network also exhibits functional differentiation among nodes and regional characteristics. The Taiwan region demonstrates notable performance in out-strength centrality (1,596 items), reflecting its advantage in copyright exports within the East Asian region. Overall, the structure follows a “core–semi-periphery–periphery” distribution pattern, illustrating the uneven global copyright trade landscape shaped by market scale, industrial capacity, and cultural influence.
Based on this calculated data and to visually compare the structural roles and functional differences of core nodes within the network, this study has created a node centrality comparison chart, as shown in Figure 2 below. The comparison chart indicates that China holds a significantly leading position in in-strength centrality (0.967), out-strength centrality (0.536), and betweenness centrality (0.318), demonstrating its absolute dominant role as the network’s core hub. Nodes representing Africa and Europe show prominent performance in in-strength (0.393) and betweenness centrality (0.274), indicating their strong function as regional collection, distribution, and transit points. Nodes such as Japan (in-strength 0.214, betweenness 0.140) and Germany (in-strength 0.187, betweenness 0.144) exhibit more balanced characteristics as regional hubs. The overall network structure presents a hierarchical system with China as the single core supported by regional nodes at a secondary level, reflecting the highly centralized nature of global copyright trade and its associated potential structural dependency risks [39].
FIGURE 2
4.3 Analysis of node degree and strength distribution characteristics
To elucidate the underlying patterns in the network’s connectivity structure and weight distribution, this study presents histograms illustrating the distributions of out-degree, in-degree, out-strength, and in-strength. This visualization aims to intuitively reveal the homogeneity in nodal connection patterns and the heterogeneity in trade volume, thereby parsing the deeper characteristics of the network topology where structural symmetry coexists with weight-based imbalance.
4.3.1 Out-degree distribution analysis
As shown in Figure 3 below, the distribution of node out-degree values exhibits a pronounced right-skewed pattern. In the sample, the number of nodes with an out-degree value of 2.5 is the largest, reaching 10, while the counts of nodes with out-degree values of 5.0 and 7.5 are 7 and 3, respectively, demonstrating a clear decreasing trend. It is noteworthy that there exists an extreme node with an out-degree value as high as 20.0, which stands in sharp contrast to the low out-degree values of the majority of nodes. According to the statistical information, the skewness of this distribution is 3.61 and the kurtosis is 12.61, quantitatively reflecting its strongly right-skewed and leptokurtic nature with heavy tails. The difference between the mean (3.82) and the median (3.0) also visually indicates the asymmetry of the distribution. This chart suggests that in the establishment of copyright export relationships, the connectivity scope of most countries is relatively limited and similar, while there exist a few exceptional nodes with anomalously large numbers of connections.
FIGURE 3
4.3.2 In-degree distribution analysis
As shown in Figure 4, the bar chart of in-degree distribution reveals a pattern highly similar to that of the out-degree distribution. The in-degree values of nodes are likewise concentrated in the low-value range, with approximately 9 nodes having an in-degree of 2.5 and about 7 nodes having an in-degree of 5.0. Similarly, there exists an isolated node with an in-degree of 20.0 in this distribution. Its statistical characteristics, such as skewness (3.61) and kurtosis (12.83), are nearly identical to those of the out-degree distribution. The mean (3.02) and median (3.0) are also very close. This chart confirms that, in terms of the establishment of copyright import relationships, the network exhibits a topological pattern symmetrical to that of the export side—that is, most countries import copyrights from a similar number of sources, resulting in a relatively uniform distribution of overall connection counts.
FIGURE 4
4.3.3 In-strength distribution analysis
As shown in Figure 5 below, the histogram of in-strength distribution employs a logarithmic scale and exhibits a shape distinctly different from the degree distribution described earlier. The data indicate that the in-strength values of the vast majority of nodes are extremely low, densely clustered on the left side of the horizontal axis (the low-strength region), while the number of nodes drops sharply as the strength value increases.
FIGURE 5
Statistical metrics reveal that the mean of the in-strength distribution (13872.18) is significantly higher than its median (1584.0), with a substantial standard deviation (52872.1) and a high skewness of 4.24. To further assess the reliability of this highly right-skewed pattern, a log-log transformation was performed on the data, followed by a goodness-of-fit test. The high coefficient of determination (R2 > 0.85) from the fit supports the observation of extreme heterogeneity in flow allocation, reinforcing the conclusion that trade flows are concentrated in very few nodes. This indicates that a small number of nodes attract an exceptionally large volume of copyright imports, whereas the import scale of most nodes remains very small. Consequently, the flow distribution is highly uneven, exhibiting characteristic features of a power-law distribution.
4.3.4 Out-strength distribution analysis
As shown in Figure 6, the out-strength distribution histogram also indicates a high degree of data concentration. Most nodes have out-strength values clustered around the order of 103, forming a broad primary peak. Its mean (13,872.19) is likewise significantly greater than the median (4,560.0), with a skewness of 3.11, indicating a right-skewed distribution. A similar goodness-of-fit test on the log-transformed out-strength data also yielded a high R2 value, confirming the robustness of the observed concentration pattern. Although the concentration trend is slightly less pronounced compared to the in-strength distribution, it still clearly demonstrates that copyright export flows are predominantly driven by a subset of nodes rather than being uniformly distributed.
FIGURE 6
4.3.5 Analysis of temporal comparison of network structure
As shown in Figures 7, 8. To observe potential evolutionary trends in the network, we divided the study period into two phases: the first half (2015–2019) and the second half (2020–2024). Separate ego-centric networks were constructed for each phase, and the centrality indicators of core nodes were calculated. A preliminary comparison indicates that the centrality positions of core nodes such as the United States and the United Kingdom remained stable across both periods.
FIGURE 7
FIGURE 8
Meanwhile, the connection strength between China and some emerging market partners showed signs of growth in the later period. This exploratory analysis suggests that while the core dependency structure exhibits persistence, marginal adjustments are occurring. A more dynamic analysis of network evolution is identified as a direction for future research.
4.3.6 Comprehensive analysis
Combining the six aforementioned charts for analysis clearly deconstructs the disjuncture between the “formal connectivity” and “substantive flows” dimensions of the copyright trade network. First, the out-degree and in-degree distribution diagrams indicate that the network exhibits topological symmetry. Most countries establish or receive a similar and limited number of copyright trade relationships. This forms a relatively uniform underlying skeleton of connections. However, the in-strength and out-strength distribution diagrams reveal a completely different picture. The distribution of trade flows is highly uneven. The vast majority of scale is concentrated in a very few nodes, whether in terms of imports or exports. This contrast illustrates a key structural feature. Although the number of trade relationships may not differ greatly, the actual trade flows carried by each relationship vary immensely.
Consequently, the network exhibits a complex structure. It is characterized by the coexistence of “broad but weak connections” and “highly concentrated strong flows”. Its core feature lies not in the variation in connection numbers, but in the extreme heterogeneity in flow allocation. This means there are minimal differences in connection numbers but significant heterogeneity in trade weights.
The exploratory temporal analysis further enriches this understanding. The centrality positions of core nodes such as the United States remained stable across two sub-periods (2015–2019 and 2020–2024). This confirms the persistence of the concentrated dependency structure within the network’s core. Meanwhile, signs of growth in connection strength with some emerging partners suggest marginal adjustments are occurring at the periphery.
5 Research conclusions and policy recommendations
5.1 Research conclusions
Based on data from China-foreign copyright trade between 2015 and 2024, this paper constructs the cross-country flow of copyrights as a directed and weighted complex network. It systematically examines the structural characteristics and power distribution of the global copyright trade system from the perspectives of topological structure, node positions, community patterns, and network resilience. Integrating the findings, the paper presents the following four main conclusions.
First, the global copyright trade network exhibits pronounced complex network properties in its overall structure. On one hand, the network displays “small-world” characteristics. It maintains relatively short average path lengths despite a high clustering coefficient. This indicates that copyright works can achieve cross-regional diffusion through limited intermediary chains. On the other hand, the network also demonstrates “scale-free” or strong heterogeneous features. Connections are highly concentrated among a few hub nodes. The network structure is not uniformly distributed but forms a clear hierarchy and asymmetric pattern. This leads to a coexistence of diffusion efficiency and power concentration: while transmission paths appear efficient, channel control is often monopolized by a minority of nodes.
Second, key positions within the network are highly concentrated in a few nodes with high betweenness centrality. This is particularly true for traditional cultural powers such as the United States and the United Kingdom. Unlike mere trade volume or output scale, betweenness centrality captures a node’s potential as an intermediary or bridge within the network topology. When certain countries lie on a large number of shortest paths, the positions they occupy provide potential advantageous channels. These channels can shape cooperative options and influence rules and standards. This network positional advantage forms an important foundation for structural power that surpasses trade volume. It possesses greater durability and reproductive capacity. Even when trade volumes fluctuate, key nodes may maintain their structural influence through these positional advantages.
Third, China exhibits a structural dilemma of being “large but not strong” within the network. China’s copyright trade connections are extensive, with a high degree of participation, and its overall scale has expanded significantly over the decade. However, its network positional advantages have not kept pace with this scale: it still faces structural constraints in accessing critical channels and bridging across communities, reflected in strong reliance on existing core hubs and relatively insufficient control over multi-community connections. The prominent issue is not merely the quantitative “trade deficit”. More importantly, it lies in China’s relative weakness in key network channels and bridging positions. This constitutes a structural constraint on improving its status within the system. Without altering connection patterns and channel structures, merely pursuing output growth may struggle to improve its status.
Fourth, the overall resilience of the global copyright trade network is relatively weak, and systemic risks cannot be overlooked. Due to the high concentration of network connections and the dependence of critical channels on a few hub nodes, once core nodes experience functional impairment or external shocks, risks are more likely to diffuse along network paths and trigger chain reactions. In such scenarios, countries at the periphery or in highly dependent positions are more likely to bear the concentrated impact of risks. Thus, the structural imbalance not only leads to asymmetric distribution of benefits and influence. It may also amplify systemic vulnerability under shock scenarios.
In summary, the core argument is that global copyright trade exhibits deep-seated structural imbalances. These cannot be explained by short-term fluctuations but are entrenched by the concentration, hierarchy, and path dependence of the network structure. As a result, a minority of countries can leverage their network positions to wield structural power that surpasses mere trade volume. They continuously shape the direction, efficiency, and boundaries of cultural flows in the long-term evolution of the system.
5.2 Policy recommendations
The structural risks revealed in this study are rooted in the inherent scale-free properties of the global copyright trade network and the resulting distribution of power. The degree distribution test of the network confirms that its connections are highly concentrated in a few hub nodes, forming a distinct core-periphery structure and a hierarchical asymmetric pattern. Within this topology, traditional cultural powers, represented by the United States, occupy positions of high betweenness centrality in the network due to their industrial foundation and first-mover advantages. This “control of channels” grants them structural power that surpasses mere trade volume, enabling long-term dominance over the critical pathways of cultural flow.
Simultaneously, the distribution of node strength exhibits a highly right-skewed pattern, with the vast majority of partner nodes having extremely low trade flows. This confirms the high concentration of flow within a very small number of nodes, constituting the micro-foundation of risk concentration.
China’s network position is characterized as “large but not strong,” meaning that the quantitative growth achieved through extensive connectivity has not translated proportionally into control over key channels. Its dependence on core hubs constitutes its structural dilemma. Furthermore, the high concentration of network connections also results in overall weak resilience, where disturbances to core nodes can easily trigger systemic risks.
To mitigate the aforementioned structural risks and propel China’s transition from a “scale advantage” to a “positional advantage” within the network, policy design should focus on proactively optimizing the deep network structure:
First, implement a precision diversification strategy guided by node centrality. Policy should systematically cultivate alternative supply and demand nodes based on the specific ranking of in-strength and out-strength centrality [40]. The objective is to reduce the excessive dependence of key copyright trade flows on a single super-hub, dispersing risks by increasing redundant connections, thereby enhancing the substitutability and recovery capacity of the network when facing shocks.
Second, pursue a “bridge-building” strategy oriented toward community connectivity. In response to the imbalanced pattern where dependencies lean heavily toward specific cultural-legal blocs, the export strategy must move beyond single-point breakthroughs in traditional core markets. It is essential to proactively establish deep, institutionalized copyright cooperation with emerging cultural blocs, such as those along the “Belt and Road” initiative. By increasing the density and stability of connections with these communities, China can transform from a “peripheral exporter” into a key intermediary organizing cross-community flows, thereby attaining higher betweenness centrality and channel control within the network.
Third, focus on specific subnetworks like digital content to first establish core node advantages. The overall structural reshaping of copyright trade requires support from sustainable business models. Priority can be given to seeking breakthroughs in the digital content sector, which features high cross-border circulation efficiency. This involves supporting the internationalization of relevant platforms and the standardization of copyright data, encouraging them to form stable cooperative nodes with overseas regional markets, with the aim of first establishing and consolidating China’s “node advantage” within specific, segmented trade networks.
6 Conclusion
In light of the aforementioned findings, this paper summarizes the policy recommendations into an overarching framework of “stabilizing the core, expanding into emerging markets, and building bridges.” The aim is not merely to pursue quantitative growth in trade volume, but to optimize China’s structural position within the global copyright trade network, thereby enhancing the resilience and effectiveness of national cultural dissemination.
By “stabilizing the core,” we refer to consolidating the quality of cooperation and institutionalized channels with traditional core markets while reducing the vulnerability arising from over-reliance on single pathways. “Expanding into emerging markets” entails proactively diversifying both import and export arrangements toward emerging content markets and non-core hub countries, fostering alternative sources and incremental cooperative opportunities. “Building bridges” emphasizes shaping China into a key node connecting different communities through regional collaboration, platform coordination, and the development of copyright service systems, thereby strengthening its capacity to organize channels for cross-community dissemination.
Through this integrated approach, China can gradually accumulate positional advantages within a structurally entrenched copyright trade system and accomplish the transition from “scale participation” to “structural shaping.”
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
XZ: Writing – original draft, Conceptualization, Investigation. WQ: Software, Writing – original draft, Investigation, Methodology. HL: Methodology, Data curation, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This research is supported by the School of international law, Zhongnan University of Economics and Law. Doctoral Research Initiation Fund Program: Intellectual Property Administrative Protection from the Perspective of the New Development Concept.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
complex networks, copyright trade, ego-centric network, international law, network resilience
Citation
Zhang X, Qi W and Liang H (2026) Structural measurement and resilience of China’s copyright trade dependency network under international regulation: a directed weighted network analysis. Front. Phys. 14:1815539. doi: 10.3389/fphy.2026.1815539
Received
23 February 2026
Revised
01 April 2026
Accepted
08 April 2026
Published
30 April 2026
Volume
14 - 2026
Edited by
Chengyi Xia, Tianjin Polytechnic University, China
Reviewed by
Yasuko Kawahata, Rikkyo University, Japan
Minyu Feng, Southwest University, China
Updates
Copyright
© 2026 Zhang, Qi and Liang.
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*Correspondence: Han Liang, 18883321210@163.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.