Structural Evolution of the Global Lithography Equipment Trade Network : Implications for Smart-City Supply-Chain Resilience

1. Introduction

Smart cities increasingly rely on chip-centered digital infrastructure, including Internet of Things devices, intelligent transportation systems, urban sensing networks, edge-computing facilities, and data centers[1]. This dependence improves urban operational efficiency, but it also brings the infrastructure vulnerability [2]: disruptions in upstream digital-technology supply chains may be transmitted downstream and affect the stable operation of smart-city systems. Among the upstream foundations of smart-city digital infrastructure, semiconductors are particularly critical. They support not only computing and communication systems, but also sensors, intelligent terminals, automated-control systems. Industry reports by the Semiconductor Industry Association and Boston Consulting Group suggest that the global semiconductor supply chain is shifting from a purely efficiency-oriented configuration toward a resilience-oriented configuration under heightened geopolitical and regulatory pressures[3]. Recent studies on semiconductor supply-chain resilience show that geopolitical tensions, export controls, and capacity shortages have become major risk sources. Xiong et al.[4] synthesized the evidence on semiconductor supply-chain disruptions and point out that vulnerabilities are embedded in the highly specialized and globally distributed structure of the industry. Moktadir et al.[5] identified geopolitical tensions as one of the most influential factors affecting semiconductor supply-chain resilience.

Lithography equipment occupies a particularly strategic position in the semiconductor supply chain. As a critical manufacturing technique, advanced lithography directly shapes wafer-fabrication capability and influences the performance and technological upgrading of chips[6]. Recent trade network evidence further shows that the global trade of lithography machine is highly concentrated among a small number of core economies, with strong path dependence and significant institutional constraints such as the Wassenaar Arrangement[7]. Therefore, risks of lithography equipment trade networks may represent upstream technological bottlenecks that affect semiconductor manufacturing capacity and the security of downstream digital infrastructures. Recent research on semiconductor supply networks has increasingly shifted from firm-level or product-level analysis to network-level vulnerability assessment. Yu et al.[8] constructed a directed weighted network of semiconductor materials and assessed its structural resilience and vulnerability. Liu et al. [9] examined the robustness of chip trade networks by incorporating topology and cascading risk propagation. These studies suggest that semiconductor-related risks should be understood not only as isolated supply interruptions, but also as systemic risks that may diffuse through trade networks.

Existing research has provided important insights into the structure of semiconductor trade networks. Using complex network analysis, scholars have examined network features, community structure, and node role changes in the global semiconductor industry. Ou et al. [10] analyzed the patterns of the global semiconductor productions (involving raw materials, mechanical equipment, and finished products) based on trade networks. It shows that semiconductor productions are embedded in a complex international division of labor. Li et al. [11] constructed a global semiconductor trade network covering raw materials, equipment, and components, revealing the structural features and robustness of semiconductor trade networks from an industry-chain perspective. Furthermore, Zhang and Zhu[12] examined that the equipment trade network exhibits a pronounced core-periphery hierarchy, with trade linkages highly concentrated among a small number of technological countries. Policy-oriented studies have also mapped cross-country dependencies in semiconductor value chains[13]. These studies demonstrate that the semiconductor trade system is not evenly distributed, but is shaped by concentration, hierarchy, and differentiated dependence across industrial-chain segments.

Related studies have also shown that semiconductor trade networks are increasingly shaped by alliance formation and geopolitical fragmentation[14][15]. Indicators such as modularity, the trade proportion of intra or inter community , and block-network sparsification are commonly used to characterize community differentiation and spatial agglomeration. Further studies have applied Exponential Random Graph Models (ERGMs), considering explanatory variables such as geographical distance, institutional ties, and geopolitical shocks, to reveal the evolutionary mechanisms of trade networks[16]. Fu and Ding’s study shown that the community structure of the chip trade network exhibits a multi-centric hierarchical pattern characterized by “core-subcore-periphery”[17]. Some studies have examined the propagation mechanisms of external shocks within trade networks[18], and investigated how factors such as national economic development, international market openness, and technological innovation capacity shape semiconductor trade structures[19]. These studies provide useful references for understanding the spatial structure of high-technology equipment trade networks.

Nevertheless, two limitations remain in the existing literature. First, existing studies often describe network structure through static or cross-sectional indicators, while paying less attention to the timing and mechanisms of long-term structural change. In particular, it remains unclear when significant structural breaks occur in the lithography equipment trade network, how these breaks correspond to external shocks such as geopolitical tensions, institutional linkages, or export-control constraints, and how such changes alter the network’s vulnerability. Second, existing studies have not sufficiently identified the dynamic shifts in network power centers and changes in critical trade channels. There remains a lack of systematic explanation of how external shocks jointly shape alliance formation, fragmentation, and restructuring in the lithography equipment trade network.

From a topological perspective, a highly centralized network may offer coordination advantages under normal conditions, but it may also increase systemic vulnerability when critical hubs, suppliers, or intermediary links are disrupted[20]. Therefore, topological analysis is useful for identifying structural dependence. This is particularly relevant for smart-city infrastructure risk management, because disruptions in upstream semiconductor manufacturing equipment may reduce chip supply stability and delay the upgrading of digital infrastructure. From a spatial-structural perspective, chip trade robustness indicates that trade relationships are not only determined by market efficiency, but also by geographical proximity, technological capability, institutional ties, and policy shocks[21][22]. In this context, community detection and role classification can be used to examine whether the trade network is evolving toward more cohesive communities, whether power centers are shifting among major economies, and whether bridge countries or critical channels are becoming more important. Such analysis can reveal the spatial logic of network restructuring.

Against this background, lithography equipment as a highly strategic upstream segment, which may differ from general semiconductor trade networks because of its stronger technological exclusiveness, higher market concentration, and greater sensitivity to export-control constrains. This study investigates the structure of global lithography equipment trade network from both topological and spatial perspectives. First, it characterizes the long-term evolution of the network’s topological structure and identify potential structural breaks. Second, it examines the spatial restructuring of the network through community detection, node-role classification, and changes in critical trade channels. Third, it interprets how geopolitical shocks, institutional linkages, and export-control constraints may jointly restructure the network.

The main contributions are as follows. First, this study develops a topological analysis framework that integrates structural break detection with event mapping. Unlike conventional cross-sectional comparisons across selected years, this study identifies structural breakpoints in the trade network over a continuous time series, thereby providing temporal evidence for characterizing the evolutionary process. Second, this study develops a dynamic explanatory mechanism for the reconfiguration of the spatial pattern of trade networks. Specifically, it examines community restructuring and power shifts in the lithography equipment trade network. By integrating the timing of structural breaks with the process of spatial pattern adjustment, this study deepens the explanation of spatial reconfiguration mechanisms from three dimensions: alliance adjustment, node-role evolution, and critical channel change.

The contribution of this study to smart-city infrastructure risk management lies in its upstream perspective. By revealing the concentration, dependence, community structure, and possible restructuring mechanisms of the lithography equipment trade network, this study provides empirical evidence for identifying upstream supply-chain vulnerabilities that may affect the resilience of chip-centered digital infrastructure. This perspective can support more forward-looking risk assessment and resilience-oriented planning for smart-city infrastructure systems.

2. Methodology

Based on global trade data of lithography equipment, this study constructs both weighted directed and weighted undirected networks. It develops an integrated three-step analytical framework, as illustrated in Figure 1. First, a static topological analysis is conducted to characterize the network in terms of scale, connectivity, reachability, and concentration. Second, structural break detection is applied to identify years in which the network undergoes significant topological change. Third, a stage-wise spatial analysis is performed to trace changes in community structure, member migration, and power shifts. Through this stepwise design, the analysis connects network topology, temporal transition, and spatial reconfiguration, thereby providing the methodological basis for evaluating how upstream trade dynamics may affect the resilience of chip-centered smart-city digital infrastructure.

2.1. Data Sources and Preprocessing

Global trade data of lithography equipment (HS code: 848620) are obtained from the United Nations Commodity Trade Statistics Database (https://comtrade.un.org/) for the period 2010-2024. Records with missing values are removed, and annual country-level trade networks are constructed accordingly.

2.2. Network Construction

(1) Weighted Directed Network

Based on the trade import-export relationships in the lithography industry among countries, this study designs a weighted directed network G = (V, E, W) using graph theory. The node set $\mathrm{V}=\left\{{\mathrm{v}}_1,{\mathrm{v}}_2,\dots ,{\mathrm{v}}_{\mathrm{n}}\right\}$ represents all countries participating in the global trade of the lithography industry. The edge set $\mathrm{E}$ consists of ordered pairs of nodes, denoted as $(\mathrm{u},\mathrm{v})$, representing the export trade relationship from country $\mathrm{u}$ to country $\mathrm{v}$. The weight function $\mathrm{w}$ quantifies the trade volume for each edge. For example, $\mathrm{w}(\mathrm{u},\mathrm{v})$ indicates the export volume from country $\mathrm{u}$ to country $\mathrm{v}$.

(2)

Weighted Undirected Network

To characterize the overall intensity of trade linkages, this study further constructs a weighted undirected network. For any pair of nodes $(\mathrm{u},\mathrm{v})$ in the network, the export value from country $\mathrm{u}$ to country $\mathrm{v}$ and the export value from country $\mathrm{v}$ to country $\mathrm{u}$ are summed to define the edge weight of the node pair $(\mathrm{u},\mathrm{v})$.

2.3. Network Topological Metrics

This study characterizes the topological features of the global lithography equipment trade network from four dimensions: network scale, structural connectivity, network reachability, and trade concentration. The definitions are presented in Table 1. Network scale serves as a indicator of whether the trade network is expanding or contracting. Structural connectivity reflects the richness of connections among nodes. Network reachability captures the efficiency of which resources or shocks can spread through the network. Trade concentration helps identify potential single-point vulnerabilities and major sources of systemic risk.

2.4. Spatial Evolution Analysis

First, this study identifies the structural breaks of the global lithography equipment trade network based on the time series of topological indicators. Second, it analyzes the community structure, member migration, and power shifts of the trade network across different break stages, revealing the evolutionary process of the spatial pattern within the global lithography equipment trade network.

2.4.1. Change-Point Detection

First, all the topological indicators are standardized using z-score normalization to eliminate scale effects. Principal component analysis is applied to extract the first three principal components. Based on the resulting principal-component score series, structural break detection is performed using the Pruned Exact Linear Time (PELT) algorithm with an L2 cost function[23].

2.4.2. Community Detection

To avoid interference from incidental fluctuations in a single year, this study constructs observation windows covering the three years for each break point, and builds weighted directed networks for each window. Following Traag et al.[24], the Leiden algorithm is adopted as the primary method of community detection , while the Louvain algorithm is used for robustness checks. Normalized Mutual Information (NMI) is employed to quantify the consistency of the community partitions obtained from the two algorithms.

Considering the community labels generated by the Leiden and Louvain algorithms are random, this study applies the Hungarian Algorithm to optimally align community labels across adjacent windows. It enables the tracking of cross-window migration among community members.

2.4.3. Spatial Structural Metrics

As shown in Table 2, the community structure indicators characterize the alliance formation in the network and the dependency relationships among alliances. The member migration indicators capture the temporal stability of community, while the power shift indicators characterize the process of network power reconfiguration at both the node and edge levels.

To systematically reveal the underlying mechanisms of network power reconfiguration, following Guimerà and Amaral[25], this study classifies nodes into different topological roles using the within-module degree z-score (Z) and the participation coefficient (PC). Considering several node roles are rarely observed in the empirical network and are unlikely to form meaningful trade linkages, this study defines five types of edges, as shown in Table 3.

3.2.1. Community Structure Characteristics

(1) The community structure shifts from high concentration toward relative differentiation.

Figure 5a shows that the number of communities remains 2-3 across all observation windows, indicating that the global lithography equipment trade network is dominated by a limited number of core communities. Figure 5b shows a continuous decline of R__LC(the proportion of nodes in the largest community), suggesting that the control exerted by a single dominant community over global trade is weakening. This change is not merely the result of spontaneous market differentiation. Rather, it is closely associated with intensifying geopolitical competition, strengthened institutional constraints, and the continued technology controls in recent years.

(2) The trade network shifts from industrial division toward alliance configuration.

Figure 5c shows that, during the first three periods before 2018, the modularity continued to decline, indicating that community boundaries were not yet clearly defined. This period coincided with the commercialization of EUV lithography equipment, during which core equipment supply, component provision, and end-market demand remained strongly interconnected at the global scale, giving the trade network an integrated structure. In the fourth period, the modularity increased significantly and remained at a high level in the fifth period. Meanwhile, T__inter (the proportion of inter-community trade value) continued to rise as shown in Figure 5d. This indicates that community boundaries were increasingly reinforced while inter-community linkages were also more intensive. This shift is highly consistent with the escalation of U.S.-China technological competition since 2018. In particular, after allies such as the Netherlands and Japan successively introduced related restrictions, the global lithography equipment trade network began to shift from the industrial division of labor toward a reorganized configuration jointly shaped by geopolitical competition, institutional constraints, and technology controls.

(3) Communities become more internally cohesive, while inter-community increasingly relies on critical channels.

Figure 5e shows that R__ID (the ratio of intra to inter community edge density) is greater than 1 across all observation windows, indicating that intra-community linkages are consistently stronger than inter-community linkages. During the first three periods before 2018, R__ID continued to increase, while T__inter (the proportion of inter-community trade value) remained relatively low. This suggests that early network evolution was primarily characterized by the stable internal coordination relationship. In the fourth period, R__ID declined slightly, where T__inter increased markedly, indicating that under global shocks such as the escalation of U.S.-China technological competition, the COVID-19 pandemic, and the global chip shortage, the lithography equipment trade network maintained operation by strengthening inter-community linkages. In the fifth period, both R__ID and T__inter increased simultaneously, suggesting that the lithography equipment trade network entered a new stage characterized by stronger internal cohesion and more critical external linkages. This indicates that, after the United States further tightened semiconductor export controls against China in October 2022, followed by allies such as the Netherlands and Japan, the lithography equipment trade network did not become genuinely fragmented, but maintained connectivity through more critical high-value channels.

3.2.2. Member migration Process

Figure 6 illustrates the member migration process between adjacent observation windows. The horizontal axis represents the community labels in the next window, while the vertical axis represents the community labels in the preceding window. The value in each cell indicates the number of same community members in adjacent windows (N__S). Lighter colors indicate a larger scale of migration.

Figure 6 shows that the community reconfiguration of the global lithography equipment trade network underwent three stages: from “stable continuity” to “local adjustment” and then to “deep restructuring.”

(1) Structural consolidation under the dominance of global industrial division

Stage 1 (Figure 6a,b): both the community composed of importing countries and the supply-oriented community dominated by Japan, the United States, South Korea, and the Netherlands retained a high proportion of stable members. This indicates that, during this stage, the global lithography equipment trade network primarily operated around a structure of “import demand-core supply-peripheral attachment”. This pattern is consistent with the deep globalization of the semiconductor industrial chain, in which countries greatly emphasized on efficiency allocation and market coordination.

(2) Local supply-chain adjustment under U.S.-China technological competition

Stage 2 (Figure 6c): the number of stable members declines markedly in both the “Europe and importing countries” community and the “Asia-Pacific supply region”. In particular, a large number of countries originally belonging to the European community migrated into the Asia-Pacific supply region, forming the most pronounced one-way migration. At the same time, China was grouped for the first time into the same community with Japan, the United States, South Korea, and Singapore, indicating strengthened trade linkages between China and core exporting countries. This stage suggests that, against the background of strengthened regional supply-chain linkages, the lithography equipment trade network began to shift toward regional agglomeration.

(3) Alliance restructuring under escalating export controls

Stage 3 (Figure 6d): the number of stable members in the original two dominant communities, namely the European and Asia-Pacific communities, continued to decline. These members were absorbed by the previously very small third community, which rapidly expanded into a new community. In particular, the United States, South Korea, and the Netherlands formed an “export-control alliance community”. This marks the transformation of the lithography equipment trade network from a “bipolar dominance and peripheral attachment” structure toward a tripartite configuration of “Europe, Asia-Pacific, U.S.-South Korea-Netherlands alliance”, indicating that the global trade system is shifting from functional integration toward institutional differentiation.

3.2.3. Power shift

(1) Power structure: the rise of East Asia, functional differentiation in Europe.

Table 5 shows that the United States and Germany consistently maintained dual-core positions across all observation windows, while China and Japan rose to dual-core status, indicating a gradual shift in the center of the global network toward East Asia. In the last period, the Netherlands, France, and Italy simultaneously rose to dual-core positions. Meanwhile, the United Kingdom, Switzerland, and Belgium became small-scale brokerage nodes, suggesting that the direct control of some traditional European core countries weakened, while brokerage nodes began to play the supplementary brokerage role.

South Korea declined from a dual-core position to an intra-community peripheral node, reflecting that, after being incorporated into a community dominated by stronger core countries, it was overshadowed by leading countries such as the United States and therefore moved to a secondary position. China’s Taiwan region remained for a long period as an intra-community peripheral node, indicating that although it is a significant manufacturing hub, it has not been able to maintain a stable core position in the network. Singapore and Malaysia rose to dual-core status in certain observation periods, suggesting that some countries can achieve stage-specific upward mobility by leveraging trade opportunities.

(2) Edge roles: a shift from “regional diffusion” to “cross-community corridors” since 2019.

Figure 7a shows the number and proportion of different edge types across observation windows, while Figure 7b shows the corresponding trade value and its proportion.

E1(channels between intra-community hubs) existed only during 2014-2018, which carried a trade value far exceeding their numerical share of edges. It exhibited a very high trade-value leverage ratio. This indicates that, during this stage, network control was highly concentrated in a small number of intra-community linkages. Since 2019, as community core nodes such as Japan, South Korea, and China were upgraded from R5 to R6, these linkages began to assume cross-community connectivity and global bridging functions. As a result, E1 edges were reclassified as E2 edges (channels between inter-community hubs), marking the transition of high-value core linkages from intra-community connections to cross-community brokerage channels. At the same time, network vulnerability shifted from localized agglomeration risk to systemic corridor risk.

E3 (channels connecting hubs and peripheral nodes), consistently accounted for the largest share of edges across all observation windows, stably carrying 44%-52% of the total trade value. This reflects the hub-and-spoke structure of the global lithography equipment trade network. Since 2019, E2 edges have expanded rapidly, indicating that cross-community corridors have become a key backbone with the highest leverage and vulnerability.

E4 (channels connecting hubs andbrokerage nodes) and E5 (channels between brokerage nodes), both gradually emerged after 2019 with limited scale. This indicates that the brokerage network functions only as a supplementary mechanism formed after the backbone network was exposed to external shocks.

(3) Critical channels: intensified core-to-core links among leading countries.

Table 7 shows the top three edges by trade value across observation windows. Overall, the critical channels underwent a upgrading process from E3 to E1 then to E2, with trade value increasing by 3.6 times. This indicates that the most important trade linkages have evolved from “the supply of core countries to ordinary manufacturing nodes” into “high-intensity connections among core countries”.

Specifically, during 2012-2016, edges such as USA→Taiwan, China, USA→South Korea, and Japan→Taiwan, China jointly supported a hub-spoke network backbone dominated by the United States, and East Asia serving as the main absorption region. During 2016-2018, the absorptive capacity of South Korea in the network increased rapidly, enabling to develop a demand center for advanced manufacturing. During 2019-2021, the key edge shifted from USA→Korea to Japan→China, and its role upgraded from E1 to E2, indicating that the diffusion relationship had transformed into a cross-community core corridor. During 2022-2024, Japan→China, Netherlands→China, and USA→China jointly constituted the most important trade channels, suggesting that the core supply channels for lithography equipment were re-established around the Chinese market. In particular, Japan→China accounted for as much as 10.5% of the total trade value, implying that any disruption to this channel would have a significant impact on the global trade, meaning that the core risk lies in the single-point disruption of a few cross-community corridors.