Complex Network-Based Resilience Assessment of the Integrated Circuit Industry Chain

Abstract

With the improvement of social production efficiency and the enhancement of the supply chain system, the traditional linear supply chain model is gradually evolving into a more complex and dynamic industrial chain network. This article uses complex network theory combined with the basic attributes of the industrial chain and supply chain to conduct a comprehensive and in-depth analysis of the integrated circuit industry chain. Firstly, a cooperative network model of the integrated circuit industry chain in Shaanxi Province is established based on the supply chain relationships of enterprises. Secondly, the study analyzes the basic characteristics of the collaborative network model. Thirdly, this study explores the efficiency, resilience, and innovation capacity of industrial chains using a novel set of indexes: the industry chain efficiency index (ICEI), the industry chain resilience index (ICRI), and the industry chain innovation capability index (ICICI). By employing principal component analysis (PCA), the study provides a comprehensive evaluation of industrial chain performance. The findings reveal that the ICEI highlights the critical importance of average path length and network density, showing that shorter paths and higher density are associated with greater efficiency. The ICRI emphasizes the roles of average degree and standard deviation, indicating that higher connectivity and lower variability contribute to resilience. The ICICI identifies the clustering coefficient and network density as key factors, suggesting that tight-knit networks foster innovation. These results offer significant insights into the dynamics of industrial chain collaboration and provide practical recommendations for enhancing supply chain management. Finally, the effectiveness of the proposed method is demonstrated through a case study. The results of the case study indicate the following: (1) Key Enterprises’ Identification: The analysis identified key enterprises like Samsung Semiconductor and HT-tech with the highest betweenness centrality, highlighting their crucial intermediary roles within the network; (2) Efficiency and Innovation Assessment: Compared with foreign-owned and other immigrant businesses, local businesses generally perform below average in terms of efficiency and resilience, indicating that there is room for improvement in technology adoption and innovation capabilities.

1. Introduction

In the context of globalization and informatization, supply chain management is rapidly evolving towards integration and intelligence. This change means that companies must enhance the transparency, coordination capability, and technological integration of their supply chains to maintain competitiveness and market sensitivity [1]. Meanwhile, it also presents some challenges for supply chains, such as increased complexity due to globalization, uncertainty in trade policies, heightened demands for environmental sustainability, and supply chain disruptions and fluctuations caused by global events (such as the COVID-19 pandemic). These trends and challenges are prompting companies to reconsider and adjust their supply chain strategies [2]. Additionally, furthermore, to adapt to market changes and consumer demands, production, supply, and distribution are becoming more closely interconnected, forming a highly interconnected industrial ecosystem [3].

This evolving environment highlights the importance of collaborative research on industry chains. Traditional supply chain management research focuses on optimizing processes within a single enterprise, but in the current globalized market environment, this is no longer enough to deal with the growing external complexity and uncertainty. Therefore, the research focus has turned to collaboration throughout the industry chain, including how to more effectively manage and coordinate relationships between different enterprises. Although industrial chain collaboration is developing rapidly as a research field, it still faces some key issues and challenges. For example, the issues of how to quantify and evaluate collaboration effects, how to identify and strengthen key nodes in the industrial chain, and how to respond to external shocks and changes require more in-depth research and exploration.

Although research has proposed a variety of theories and models to promote collaboration among industrial chains, the application effects of these theories and models still vary widely in different industries and environments. For instance, Liu et al. [4] investigated the complexity of supply chain collaborations and emphasized the need for dynamic approaches that consider varying cooperation behaviors and partner characteristics, which are often overlooked in existing models. Similarly, Sudusinghe et al. [5] highlighted that current models frequently lack statistical validation and fail to capture the complexities of real-world supply chain networks. Furthermore, Ftikhar et al. [6] identified the diverse impacts of collaboration mechanisms across different industries, suggesting that contextual differences significantly influence collaboration outcomes. These limitations underscore the necessity for context-specific empirical research to develop and validate practical models that can effectively guide industrial chain collaboration in diverse environments. This suggests that the understanding of industrial chain collaboration mechanisms is not yet comprehensive, and further empirical research is needed to explore the best practices for collaboration in different situations. It is against this background that this article chooses complex networks as an analysis tool to deepen our understanding of industrial chain collaboration by revealing the complex interdependencies and dynamic changes in the industrial chain and to improve the competitiveness and competitiveness of the overall industrial chain. To delve deeper into the characteristics of industrial chain collaboration, this paper selects complex networks as the analytical tool. A complex network is a mathematical model that can describe intricate relationships between a large number of interacting elements. Through complex network theory, the structural characteristics of various nodes and edges in the industrial chain, such as degree distribution, clustering coefficient, and average path length, can be revealed. These characteristics reflect properties of the industrial chain like small-world, scale-free nature, and clustering; these properties help us to assess the efficiency, stability, resilience, and innovation capacity of the industrial chain [7]. Secondly, complex network theory can use methods such as community detection, core–periphery structure, and centrality to identify key nodes and subnetworks in the industrial chain, such as leading enterprises, innovation centers, and collaborative groups. These methods can help to optimize the configuration and management of the industrial chain, enhancing its competitiveness and synergistic effects. Finally, complex network theory can aid governments or enterprises in analyzing and responding to changes and challenges within the industrial chain, promoting its development and upgrade.

The integrated circuit industry chain presents complex interdependencies and dynamic changes that necessitate a deep understanding of collaborative mechanisms. Therefore, this study aims to investigate the collaborative mechanisms within the integrated circuit industry chain. Specifically, the research examines how different collaboration mechanisms within the integrated circuit industry chain affect the resilience, efficiency, and innovation capabilities of enterprises and identifies the best practices for enhancing these attributes in diverse operational contexts.

Compared with current research, this study aims to propose and verify a comprehensive index system, including the industry chain efficiency index (ICEI), industry chain resilience index (ICRI), and industry chain innovation capability index (ICICI). These indices not only cover traditional efficiency and resilience evaluations but also innovatively add the measurement of supply chain innovation capabilities. Using a method based on principal component analysis (PCA), this study reduces data dimensions while retaining the main information, thereby providing a more comprehensive and accurate evaluation framework for supply chain performance. Additionally, appropriate management suggestions are put forward based on case data.

This paper takes the Shaanxi region of China as the research object and uses complex network theory to establish a collaborative network of the integrated circuit industry chain. The chapters of this article are organized as follows: Section 2 briefly outlines the current research status of supply chain and industrial collaboration and the application of complex networks in industrial chains. Section 3 introduces the method and steps of building a collaborative network in this article. Section 4 discusses the main characteristics, connotations, and basic attributes of the integrated circuit industry cooperation network in Shaanxi Province. Section 5 demonstrates the feasibility of the proposed method through cases. Finally, Section 6 discusses the significance of the research results of this article and feasible suggestions for the development of integrated circuits in Shaanxi Province.

2. Literature Review

As global competition intensifies and new technologies continue to emerge, such as cloud computing, the Internet of Things, big data, artificial intelligence, blockchain, etc., these technologies provide new platforms and opportunities for collaborative innovation in the industrial chain. However, problems such as information asymmetry, lack of trust, and knowledge protection often arise in the process of collaborative innovation [8]. Many scholars mainly solve these problems from three aspects, thereby improving the competitiveness and sustainable development capabilities of the industrial chain.

2.1. Maturity Model

One solution is to build a maturity model. To evaluate and improve the level of industrial chain collaborative innovation, some researchers have proposed a maturity model based on the capability maturity model integration method, which can be used to analyze the different stages of industrial chain collaborative innovation, as well as the goals and objectives that need to be achieved at each stage. Correia et al. [9] conducted a systematic literature review on maturity models and their application to supply chain sustainability between 2000 and 2015, and they found 11 studies aimed at developing new maturity models. They analyzed the characteristics, structure, methods, and evaluation indicators of these models and proposed some future research directions. Furthermore, Correia et al. [10] developed a model for assessing supply chain sustainability maturity levels; the model is designed to help companies to identify their strengths and weaknesses in supply chain sustainability and develop corresponding improvement plans. Rakesh and Agarwal [11] proposed a framework to improve the effectiveness of university-industry collaboration (UIC). The framework can help universities and industries to assess their current practices and identify areas for improvement in their collaboration. Arun Kumar et al. [12] explored the relationship between supply chain collaboration (SCC) mechanisms, maturity level in particular, and performance outcomes in the textile and garment industry. Susana Garrido et al. [13] proposed a framework of supply chain maturity tools to describe and analyze the current state of an organization or unit. The framework provides a structured approach to analyzing how a company meets certain requirements and identifies areas for improvement to achieve a higher level of maturity. Saverio Ferraro et al. [14] analyzed maturity models in supply chain management and logistics through a systematic literature review. The study found that in recent years there has been increasing emphasis on models for assessing Industry 4.0 readiness and sustainability principles, but there are still some shortcomings, such as insufficient attention to optimizing and integrating logistics processes, underutilized and validated models, and a lack of a comprehensive improvement guide. However, the main scope of the above research is limited to a single enterprise or case, and it cannot study the complete supply chain system.

2.2. Industry Chain Optimization

Another solution is to evaluate and optimize industry chain collaboration to guide enterprises on how to implement open supply chain innovation. In [15], the authors proposed a supply chain collaborative innovation performance evaluation system based on the product life cycle theory; they took an auto parts company as an example and used the fuzzy comprehensive evaluation method to verify the effectiveness and feasibility of the evaluation system. Through establishing a supply chain collaborative innovation efficiency evaluation model based on data envelopment analysis, Liu et al. [16] took a food company as an example, in which the supply chain collaborative innovation efficiency is divided into three aspects: technical efficiency, scale efficiency, and management efficiency. Katsaliaki et al. [17] discussed the challenges and opportunities of implementing Industry 4.0 technologies in supply chain management. The paper also provides some illustrative real-life cases of supply chain disruptions and resilience. Saurabh Tiwari et al. [18] explored the relationship between Industry 4.0 and SCI via an extensive literature review to understand the various levels of integration with the supply chain processes to identify missing links, through a framework, and suggest further research directions. Pankaj Kumar Detwal et al. [19] systematically reviewed the latest progress in sustainable supply chain management (SSCM) that combines optimization and Industry 4.0 technologies, and they proposed a conceptual framework to illustrate how these technologies can promote supply chain sustainability. Runtao Zhang et al. [20] proposed a supply chain optimization model for the steel industry based on preventive maintenance to improve the logistics supply chain by increasing transportation efficiency and testing maximum production capacity.

2.3. Complex Network Theory

In recent years, with the proposal and construction of the BA scale-free network model, more and more scholars have used the knowledge of complex networks to solve the problem of industrial collaboration. Ref. [21], in a study of the complex characteristics of supply chain networks, found that the supply chain networks that showed efficient characteristics had a degree distribution, average path length, and clustering coefficient that showed power-law distribution characteristics, and they concluded that the structure of efficient supply chain networks should conform to the “scale-free” characteristics. Yoshi Fujiwara and Hideaki Aoyama [22] built a production network based on the input–output relationship by collecting relevant data from Japanese enterprises. Through analysis, it was found that it had the characteristics of being scale-free, anisotropic matching, regional or departmental door modularization, community structure, and so on. P. Wichmann et al. [23] developed the Supply Network Link Predictor (SNLP) method to infer supplier interdependencies using the manufacturer’s incomplete knowledge of the network. SNLP uses topological data to extract relational features from the known network to train a classifier for predicting potential links. Shauhrat S. Chopra and Vikas Khanna [24] took Kalundborg Industrial Symbiosis (KIS) in Denmark as an example and used network indicators and simulation scenarios to analyze the structural characteristics and functional roles of industrial symbiosis networks, revealing the most critical nodes in the system. They proposed some design strategies, such as increasing diversity, redundancy, and multifunctionality, to improve the resilience and sustainability of industrial symbiosis networks. Lichtenstein [25] simulated the ecological factors of technological innovation clusters based on CAS theory and obtained the internal and external environment and market conditions needed for the survival and development of enterprises in the future through simulation tests, to obtain the conditions and opportunities for the emergence of technological innovation clusters. Azadegan [26] presented a typology of supply network resilience strategies, highlighting the complexity of collaborations within and between supply networks in response to significant disruptions, such as the COVID-19 pandemic. It differentiates between micro-level (direct buyer–supplier coordination), and macro-level (collaboration among competitors and institutions for long-term risk management), and introduces meso-level resilience (opportunistic, ad hoc collaborations across multiple networks for short- to medium-term risks), emphasizing the latter as a dynamic, complex adaptive system that enhances supply chain resilience through innovative, collaborative approaches. Supun S. Perera et al. [27] critically reviewed existing research on modeling supply chains as complex adaptive systems to enhance resilience. The review identifies the key methodological limitations in current models and proposes a conceptual framework that incorporates operational and topological aspects, alongside a new set of resilience metrics, to offer a more realistic representation of supply networks. Jiakuan Chen et al. [28] studied the use of complex network theory to construct weighted network models suitable for knowledge-intensive industries to assess and improve industry resilience and development. Donghui Yang et al. [29] conducted an in-depth study of the robustness structure of the supply chain and suggested focusing on establishing hub-like connections with upstream and downstream partners. These findings provide insights for automotive supply chain management and optimized network construction risk mitigation.

In summary, the above solutions provide a dynamic and feasibility analysis of industry chain collaboration from different perspectives. They have a positive impact on the innovation and optimization of industrial chain collaboration. However, there are also some disadvantages. Firstly, there is a lack of differentiated analysis of companies in different industries and sizes. Secondly, there is a lack of differentiated analysis of different sources and types of supply chain collaborative innovation risks. In this paper, complex network theory has been introduced to solve this issue.

3. Construction of Industrial Chain Cooperative Network

3.1. The Boundary of Industrial Chain and Activity Subject Analysis

Building upon the processed node data and the establishment of inter-node connections that take into account both business and geographical factors, the local supply chain network of the integrated circuit industry in Shaanxi Province is segmented into five distinct tiers. These tiers are denoted as T₁, T₂, T₃, T₄, and T₅, where T₁ through T₄ signify the upstream and midstream supply tiers, respectively, and T₅ denotes the downstream manufacturing tier. Consequently, the entire supply chain network of the electronic component industry within Shaanxi Province is thus delineated:

S_T = {T₁, T₂, T₃, T₄, T₅}

(1)

The set of upper nodes for each level is represented as Ti = {t_i1, t_i2, t_i3, …, t_in}, where T_i denotes the i-th level in the supply chain network and t-in indicates there are n nodes in the level.

In the integrated circuit sector, a multitude of enterprises engage in a variety of relationships, such as transactions, equity participations, and investments, facilitated by regular interactions [30]. The network fundamentally forms connections grounded in the visible corporate affiliations of the enterprises as well as the concealed upstream–downstream relationships within the industry. Initially, significant enterprise data are harvested utilizing a web crawler plugin, followed by the determination of relationships according to their respective positions within the supply chain. Considering the unidirectional flow of the industrial chain, a company’s financial robustness partially mirrors its clout within the network. This study examines a directed and weighted enterprise network. The organization of enterprise relationships is meticulously undertaken, with this information subsequently transformed into a matrix format for enhanced analysis. Network relationships are visualized via Gephi (Gephi-0.10.1), facilitating the generation of an electronic component enterprise network diagram. The detailed diagram of the industrial chain is presented in Figure 1.

3.2. Node Description

In the study of complex networks, nodes can be conceptualized through diverse perspectives and methodologies; however, they typically symbolize the network’s fundamental unit [31]. A node signifies an entity or element within the actual system, with connections between nodes illustrating the interactions or relationships among these entities. This research focuses on the integrated circuit industry’s cluster network, identifying nodes as electronic component enterprises and their allied support entities. As a result, the distinct attributes of these enterprises shape the node characteristics, thereby influencing certain aspects of the industry cluster network.

Integrated circuit enterprises strategically enter particular industries leveraging their comparative advantages. They accomplish their goals through collaboration with associated businesses or competition with analogous enterprises. Consequently, the majority of nodes within the industry cluster network are dynamic and selectively establish connections with other nodes. Typically, these nodes’ detailed information encompasses the names of the relevant manufacturing companies and their auxiliary businesses, their principal products, geographical locations, and commercial relationships.

The method of defining nodes plays a pivotal role in analyzing the network structure and dynamics within the integrated circuit industry cluster. This analysis aids in comprehending the interactions among enterprises, their influence, and their contributions to the broader industry ecosystem. Such insights are indispensable for strategic planning, pinpointing pivotal entities, and enhancing collaborations or alleviating competitive tensions within the sector.

3.3. Edge Description

Based on the capital relationships and supply relationships collected among the enterprises mentioned earlier, the set of network edges, denoted as E, is constructed to define the relationships between these enterprises. If all the edges in the network are represented as a collection, then it can be expressed as E = {e₁, e₂, e₃, …, e_n}.

Theoretically, within the integrated circuit industry cluster network, edges connecting nodes symbolize either competitive or cooperative dynamics among enterprises and their supporting entities. Cooperative dynamics can be delineated into tangible and intangible forms. Tangible cooperation is predominantly evidenced through transactional interactions among businesses, encompassing purchase and sale agreements, equity distributions, collaborative product development, and similar activities. Conversely, intangible cooperation is characterized by the complementarity of products or support services, and the mutual sharing of essential resources, among other aspects. Competitive dynamics are primarily defined by the potential for product or service substitution.

Given the unique characteristics of the electronic components industry, which is marked by a broad spectrum of products, a multitude of categories, and diverse levels of production complexity, coupled with the need to maintain the confidentiality of core business information, this study predominantly concentrates on the dynamics between upstream and downstream enterprises. It therefore selectively disregards the interactions among similar or homogeneous entities.

Guided by these principles, both manufacturing enterprises and their supporting entities within the integrated circuit industry cluster are designated as nodes within a complex network. The connectivity, represented by edges, for each node, is quantified by the real-world interactions among various manufacturing and support enterprises. Specifically, when a manufacturing enterprise (one node) engages in supply chain activities with a supporting business (another node), this interaction establishes an edge between the two nodes. Similarly, any interaction between entities is recognized as an edge, with the registered capital of the involved parties serving as the weight of this edge. Consequently, the complex network model of the integrated circuit industry cluster, devised following these guidelines, forms a directed and weighted network.

3.4. Description of Weights

In this study, V = {v₁, v₂, v₃, …, v_N} can be defined as the set of nodes, so v_i (i = 1, 2, …, N) can represent manufacturing and service enterprises. E = {e₁, e₂, e₃, …, e_M} represents the set of edges. In the context of enterprise social production activities, the size of a company’s registered capital can influence its status and role in the industry chain. Enterprises with a larger registered capital often have more resources, technology, market presence, and influence, enabling them to establish more cooperative or competitive relationships, thereby increasing the connectivity and stability of the industry chain complex network.

Furthermore, a company’s registered capital size serves as an indicator of its contribution and significance within the industry chain. Companies with substantial registered capital often exhibit superior production efficiency, innovative capabilities, quality control standards, and service excellence. This enables them to supply a broader array of products, technologies, and services to the industry chain, thereby augmenting the network’s benefits and sustainability.

Lastly, the magnitude of a company’s registered capital serves as a gauge of its competitive edge and advantages within the industry chain. Companies endowed with considerable capital are typically characterized by enhanced risk mitigation, adaptability, coordination, communication proficiencies, and strategic prowess. Such companies are adept at securing greater benefits and opportunities within the industry chain, consequently amplifying the network’s vitality and adaptability.

Hence, the network modeled in this research represents the size of the registered capital among enterprises as the network’s weight. Enterprises possessing substantial registered capital are likely to have superior logistics, production technology, and lower operating costs, thereby enhancing their propensity for collaboration. On the flip side, enterprises with minimal registered capital might encounter increased risks and financial constraints, which could impede their readiness and efficiency in forming partnerships.

4. The Main Characteristics and Connotations of Industrial Chain Network

4.1. Network Density

In examining the topological structure of complex networks, network density emerges as a critical metric for outlining the network’s overarching characteristics. This metric effectively reflects the frequency and intensity of interactions among the network’s constituents (nodes). As a rule, an increase in network density correlates with a heightened impact on the nodes’ activities and their mutual interactions. Networks characterized by dense interconnectivity afford their members access to diverse information resources, promoting efficient communication and the sharing of resources. This connectivity may foster synergistic effects, bolstering the network’s collective performance and capacity for innovation. Nonetheless, networks of high density may encounter drawbacks, including the risk of homogenization, where the nodes’ activities and strategies become overly uniform, diminishing diversity and possibly hindering innovation. Additionally, in such interconnected environments, disruptions or failures can swiftly spread throughout the network, posing risks to its overall stability and resilience.

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

(2)

In the above, N indicates the number of nodes in the network; M represents the number of edges in the network.

4.2. Average Network Path Length

The average path length within a network serves as an indicator of the network’s circulation and communication efficiency among nodes. A reduced average path length signifies enhanced transmission efficiency, facilitating smoother access to other nodes. Particularly in a supply chain network characterized by a reduced average path length, there is an elevation in the speed and efficiency of resource exchange and communication among businesses and nodes. Consequently, this leads to a decrease in the cost associated with disseminating information among businesses.

Nonetheless, the benefits of a shorter average path length are not without their potential drawbacks. Such reduced path lengths might result in a diminished number of connections among businesses, indicating a tight structural proximity. This proximity can facilitate the swift spread of risks and failures throughout the network. If a single node within the industrial chain experience difficulties, other businesses linked to this node will probably be promptly influenced. The absence of alternative routing paths and time delays can render businesses more reactive and susceptible. Under these conditions, issues related to connectivity may swiftly affect the local network and precipitately extend to a more expansive network domain.

Therefore, although a reduced average path length contributes to improved efficiency and accelerated communication and resource distribution, it simultaneously demands stringent risk management and detailed contingency strategies. For businesses within these networks, it is critical to establish measures that allow for the swift detection, isolation, and mitigation of disruptions, thereby reducing the likelihood of extensive consequences. Achieving a harmonious balance between operational efficiency and network resilience constitutes a fundamental aspect of both designing and administering supply chain networks.

$$L=\frac{1}{\frac{1}{2}N(N-1)}\sum _{i\ge j}{d}_{ij}$$

(3)

In the above, N indicates the number of nodes in the network; $d_{ij}$ indicates the shortest path length between node i and node j.

4.3. Clustering Coefficient

The clustering coefficient plays a pivotal role in the analysis of complex networks, serving as a measure of the closeness and the community structure within the network. This coefficient specifically gauges the level of interconnectivity or density among the neighbors of a node, offering insights into how tightly knit these groups are. Its application is especially relevant in the analysis of undirected networks, where the relationships between nodes are bidirectional.

In the context of industrial chain migration research, the clustering coefficient is employed to assess the coherence of connections and the structure of organizations within industrial chain networks. The nodes within these networks represent diverse industry segments, companies, organizations, or various entities. This coefficient is instrumental in evaluating the proximity among these nodes and their propensity to cluster into groups or form subnetworks.

An elevated clustering coefficient within an industrial chain network indicates that its nodes, comprising companies, organizations, and other entities, are closely interconnected and inclined to establish cohesive groups or clusters. This phenomenon may signal robust collaboration or mutual dependence among specific network participants. Such clustering is advantageous, as it frequently fosters synergistic relationships, resource sharing, and streamlined information exchange within these groups. Nonetheless, elevated levels of clustering are not without their drawbacks. Such high clustering may result in insularity, characterized by clusters becoming self-sufficient and less receptive to external ideas or innovations. This insularity could significantly impede the industrial chain’s overall adaptability and resilience, making these clusters more resistant to change and slower to adapt to shifts in market dynamics.

$$CC(i)=\frac{2R_i}{k_i(k_i-1)}$$

(4)

• $R_i$ indicates the number of edges connected between nodes.
• $k_i$ indicates the number of nodes.

In summary, understanding the clustering coefficient in industrial chain networks helps in assessing the nature and strength of the connections within the industry, providing insights into both the opportunities for collaboration and the potential risks associated with tightly knit clusters.

4.4. Node Betweenness

In complex networks, node betweenness quantifies the count of shortest paths passing through a particular node among all node pairs within the network. This metric serves to assess a node’s significance, reflecting its capacity for transfer and its connectivity degree. A pronounced correlation exists between a node’s degree and its betweenness, with nodes boasting higher degree values typically exhibiting elevated betweenness levels. Within the communication equipment industry’s context, betweenness delineates an enterprise’s pivotal role in the industry chain as a central node through which other enterprises access essential production factors. Essentially, this implies that other entities rely on conducting business activities or securing key resources via this enterprise to sustain their operational and production capabilities.

$$C_B(vi)=\sum _{k\ne vi\ne j}\frac{{\sigma }_{kj}\left(vi\right)}{{\sigma }_{kj}}$$

(5)

• $C_B\left(vi\right)$ represents the betweenness centrality of the company.
• ${\sigma }_{kj}$ is the total number of shortest paths from company k to company j in the network.

4.5. Industry Chain Efficiency Index

The current study introduces the industry chain efficiency index (ICEI) as a novel metric designed to quantitatively assess the overall operational efficiency of industrial chains. This index offers a holistic evaluation of efficiency by integrating considerations of both the velocity at which information and resources circulate within the industrial chain and the cohesiveness of the network structure. Specifically, the ICEI amalgamates two key parameters: the average path length, which mirrors the rapidity of information and resource transmission, and network density, indicative of the network’s structural cohesiveness. Through ICEI analysis, we can derive a detailed comprehension of the quality and efficiency of inter-enterprise interactions within the industrial chain. Elevated ICEI scores suggest enhanced rates of information and resource exchange, alongside a more interconnected network configuration, typically signifying a greater efficiency of the industrial chain. This approach aligns with the performance measures and metrics discussed by Gunasekaran et al. [32], who emphasized the importance of comprehensive evaluation metrics in assessing supply chain performance.

$$ICEL=\frac{1}{\rho }L$$

(6)

• $L$ indicates the network density in the previous section.
• $\rho$ indicates the average network path length.

4.6. Industry Chain Resilience Index

The study proposes the industry chain resilience index (ICRI), a novel quantitative measure designed to evaluate the adaptability and resilience of industry chains against a variety of shocks and changes. This indicator is crucial for understanding the industrial chain’s stability and its capacity to resist external disturbances. The ICRI’s computation leverages two principal parameters: the network’s standard deviation, which captures the variability within the industrial chain, and the average degree of the network, reflecting the strength and uniformity of connections among entities within the chain. The integration of these parameters offers insights into the cohesiveness and robustness of the industry chain’s structure. Through ICRI analysis, stakeholders can gauge the industry chain’s preparedness and responsiveness to economic volatilities, market shifts, or other unforeseen challenges. This approach aligns with Sheffi and Rice’s [33] view on supply chain resilience, which emphasizes the importance of network structure and variability in determining an enterprise’s ability to withstand and recover from disruptions. Generally, a higher ICRI value signifies a more resilient industrial chain, characterized by its strong capability to endure stresses and rebound swiftly from disruptions.

$$ICRI=\frac{1-{\sigma }^2\left(N\right)}{\overline{deg\left(N\right)}}$$

(7)

where ${\sigma }^2\left(N\right)$ represents the standard deviation of the network, which is used to measure the uniformity of network connections. $\overline{deg\left(N\right)}$ represents the average degree of the network, that is, the average number of connections per node.

4.7. Industry Chain Innovation Capacity Index

The study introduces the industry chain innovation capacity index (ICICI) as a quantitative tool to assess the innovation potential and effectiveness of industrial chains. This index provides a thorough evaluation of the industrial chain’s innovation dynamics, incorporating factors related to collaboration structure and resource distribution. The formulation of the ICICI involves key parameters such as the clustering coefficient, which signifies the level of tight-knit collaboration among entities, and the ratio of network density, indicating the overall connectedness within the chain. Additionally, the ICICI encapsulates aspects like the average degree to portray the collaboration depth and network density for a comprehensive insight into cooperative innovation capabilities. This approach aligns with Prajogo and Olhager’s [34] findings, which emphasize the importance of supply chain integration in enhancing innovation performance through long-term relationships, information technology, and logistics integration. Through detailed ICICI analysis, stakeholders can discern the intensity and quality of innovation-driven cooperation across the industrial chain. Elevated ICICI figures predominantly suggest a robust collaborative network, poised for high innovation output and efficiency.

$$ICICI=C\times (\frac{\overline{D}}{D})$$

(8)

Among them, $C$ represents the clustering coefficient, $\overline{D}$ represents the average degree, and $D$ represents the network density. A high clustering coefficient indicates the existence of tight small groups in the network, which is conducive to the flow of information and knowledge and the occurrence of innovation, while the ratio of average degree to network density reflects the overall network collaboration and resource allocation efficiency.

4.8. Comprehensive Industry Chain Performance Index

This research introduces the comprehensive industry chain performance index (CICPI), designed to evaluate the overall performance of industry chains across various dimensions comprehensively. The CICPI is calculated by combining the industrial chain efficiency index (ICEI), industrial chain resilience index (ICRI), and industrial chain innovation capability index (ICICI). These sub-indicators are given different weights according to their relative importance in the performance of the industrial chain to ensure the comprehensiveness and accuracy of the comprehensive evaluation. The design of the CICPI takes into account the various characteristics of industrial chain operations, enabling research to evaluate the efficiency, stability, and innovation capabilities of the industrial chain from a macro perspective. This comprehensive evaluation is critical to understanding the dynamic characteristics and potential improvement points of the industrial chain.

$$ClCPI=w_1\times ICEI+w_2\times ICRI+w_3\times ICICI$$

(9)

5. Case Study

5.1. The Overall Situation of the Shaanxi Integrated Circuit Industry Chain

The integrated circuit (IC) industry chain in Shaanxi Province represents a comprehensive ecosystem, spanning from the development and production of semiconductor equipment and materials to the intricate processes of design, manufacturing, packaging, testing, and system application of integrated circuits. This chain encapsulates the full spectrum of activities essential for the lifecycle of integrated circuits, underscoring the province’s pivotal role in the national IC industry landscape. As of recent evaluations, Shaanxi’s IC industry occupies a commendable position within China’s second-tier echelon, trailing behind the industry giants of Jiangsu, Shanghai, Beijing, and Guangdong.

Shaanxi’s integrated circuit industry hosts renowned domestic and international enterprises such as Samsung, Micron, Huatian, and YiSiWei, as well as local leading companies like ZTE Kerui, Unigroup Guoxin, and Torex. The products cover many fields including communication, memory, the Internet of Things, and power devices. Currently, Shaanxi’s highest level of design has reached 7 nm, and there is ongoing research and development of SoC chip design on the 10 nm industrial platform. The highest level of wafer manufacturing products is 12-inch 14 nm class memory. Relying on the research institutes and universities in Xi’an, Shaanxi’s integrated circuit industry has formed a semiconductor technology innovation platform centered around the Shaanxi Semiconductor Technology Leading Center. At the same time, through the vertical integration of “chain leader” enterprises and the collaborative win-win approach of upstream and downstream industries, Shaanxi has built an industrial chain ecosystem led by leading enterprises, featuring cluster integration and deep collaboration.

5.2. Calculation Results and Analysis of Collaboration Network Indicators of the Shaanxi Integrated Circuit Industry Chain

This article selected integrated circuit equipment manufacturing companies in Shaanxi Province with a registered capital of more than 20 million through Tianyancha screening. Since the shipments of other smaller manufacturers are very limited, the disclosure of industry chain information is also limited. It is opaque and difficult to collect more information involving business secrets. Therefore, this article selects this part of the supplier data as the research object without discussing too much about smaller manufacturers. After that, by searching and collecting public information from the official website of the core supplier company, and reading the company’s relevant public information such as annual reports of listed companies, etc., we collected and summarized a large number of detailed information about the core supplier company and its branches, as well as associated companies, production bases, and supply factories; through the connections between these information and data, the study established a topological map of the integrated circuit industry. In complex networks, there are many indicators that can reflect the importance of nodes, such as degree, weighted degree, eccentricity, closeness centrality, and so on. These indicators can be analyzed and calculated based on the basic properties of the network. Some of the important node data are shown in

Table 1. The collected enterprise data.

Company	Degree	Weighted Degree	Eccentricity	Closeness Centrality	Clustering Coefficient
SMIC	27	149	6	0.4056	0.0085
Huawei Technologies Co., Ltd.	25	182.4	3	0.8	0.0014
Samsung Semiconductor (China) Co., Ltd.	21	134	3	0.7913	0.2668
Shaanxi Zhongjun Tengda Electronic Co., Ltd.	20	107.75	3	0.5789	0.2660
Hongxin Technology Co., Ltd.	16	64	5	0.3793	0.2234
Lonten Semiconductor Co., Ltd.	16	48	12	0.1830	0
TSMC	15	78	3	0.7222	0.0083
ESWIN	14	59	10	0.1965	0
BYD Electronics (Xi’an)	14	88	5	0.3699	0
HT-tech	12	52	3	0.7059	0.5495

below.

5.3. Construction Process and Data of the Collaborative Network in Shaanxi Integrated Circuit Industry Chain

Based on the description of the model mentioned earlier, the model of the integrated circuit industry chain network in Shaanxi Province was developed using the collected data of 281 nodes and 487 edges. To facilitate visual analysis of the entire network, the generated node and edge data were imported into Gephi for processing and analysis.

This visual representation provided by Gephi allows for an intuitive understanding of the integrated circuit industry chain network in Shaanxi Province. It highlights key players in the industry and the nature of their relationships, providing insights into the network’s structure, the influence of various companies, and the dynamics of cooperation and dependency within the industry. The optimization process performed in Gephi software transformed the initial network visualization (Figure 2) into a more refined version (Figure 3).

Figure 3 provides a visual representation of the integrated circuit industry’s collaborative network in Shaanxi Province. It depicts the complex interconnections among companies, with the size and color intensity of nodes and edges indicating the centrality and interconnectedness of the companies within the network. Larger and darker nodes represent companies with a stronger comprehensive strength, higher industry reputation, and broader influence across the industrial chain. The network diagram underscores key players, illustrating the intricate web of cooperation and dependency that defines the industry’s structure and dynamics. This visual analysis aids in identifying influential entities and understanding their strategic interrelationships, which are crucial for driving innovation and growth within the region’s integrated circuit sector.

5.4. Computational Results and Analysis of Collaborative Network Metrics in Shaanxi Integrated Circuit Industry Chain

This article conducts an incisive examination of the integrated circuit industry chain’s collaborative network in Shaanxi Province by calculating critical network metrics: node out-degree, in-degree, cluster coefficient, and betweenness centrality. These metrics are essential for quantifying the network’s structural attributes and pivotal in revealing the network’s significant nodes and substructures.

5.4.1. Company In-Degree

The identification of the top 10 companies within the network, based on metrics such as centrality, underscores their pivotal role and prominence within the semiconductor industry chain.

Table 2. The in-degree of the top 10 enterprises.

Company	In-Degree
SMIC	22
Huawei Technologies Co., Ltd.	12
Samsung Semiconductor (China) Co., Ltd.	12
Shaanxi Zhongjun Tengda Electronic Co., Ltd.	11
Electronic Co., Ltd.	9
Hongxin Technology Co., Ltd.	8
Lonten Semiconductor Co., Ltd.	8
TSMC	8
ESWIN	8
HT-tech	7

presents a summary of the in-degree scores of the top 10 companies These companies, by their network positions, enjoy enhanced access to resources, information, and opportunities for collaboration compared to their counterparts. The disparities in centrality and significance among entities within the network can be attributed to several key factors:

Reputation and Brand Recognition: The leading companies are distinguished by their superior reputations and brand recognition. Entities renowned for their brand are more adept at securing collaborations and resources from other firms. A robust reputation is frequently linked to attributes such as reliability, quality, and trustworthiness, which play a critical role in fostering business partnerships.

Business Scope: Leading corporations such as Huawei, Samsung Semiconductor, SMIC (Semiconductor Manufacturing International Corporation), and TSMC (Taiwan Semiconductor Manufacturing Company) specialize in the design, research, and development, production, and foundry services of advanced chips. These firms predominantly operate within the midstream and downstream segments of the industry chain. Their strategic positioning enables them to more effectively aggregate upstream resources for production and innovation, showcasing pronounced capabilities in integration.

The strategic positions of these companies within the industry chain empower them to assume pivotal roles in resource integration and leverage. Their active participation in critical phases of the value chain, augmented by their reputational prowess, grants them substantial sway and authority within the network. This dominion extends beyond mere production capabilities; it encompasses influencing industry trends, driving technological progress, and establishing benchmarks that other industry participants might adopt.

5.4.2. Company Out-Degree

In the integrated circuit industry chain, companies occupying the top 10 positions in terms of out-degree predominantly consist of midstream manufacturing enterprises and raw material suppliers. These entities are integral to the industry chain due to multiple factors.

Infrastructure and Fixed Assets: Companies leading in out-degree frequently boast substantial infrastructure and considerable fixed assets, which are vital for their operational capacity. The array of equipment essential for the integrated circuit manufacturing process includes, but is not limited to, crystal growth furnaces, slicing machines, grinders, photolithography machines, ion implanters, etching machines, epitaxial apparatus, coating equipment, die bonders, and wire bonders. The advanced nature and dependability of such equipment critically influence the quality and volume of integrated circuit products.

Supply of Raw Materials: Additionally, these companies are pivotal in providing essential raw materials required for the production of high-quality integrated circuits. This includes single-crystal silicon, large silicon wafers, target materials, special gases, chemicals, lead frames, metal wires, and encapsulation materials. The quality of these materials, along with the stability of their supply, is crucial for ensuring the seamless operation of the entire industry chain.

Services for Downstream Industries: The offerings of these companies extend vital support to downstream sectors involved in packaging, testing, and the manufacturing of end products. Beyond supplying the requisite materials and equipment for these subsequent phases, they also facilitate efficient and seamless operations by providing technical support and services.

Thus, midstream manufacturing enterprises and raw material suppliers hold a pivotal role within the integrated circuit industry chain. Their importance transcends mere production and supply chain functions; they are instrumental in upholding the stability and operational efficiency of the entire industry chain.

Table 3. The out-degree of the top 10 enterprises.

Company	Out-Degree
SMIC	18
Samsung Semiconductor (China) Co., Ltd.	12
ESWIN	11
Lonten Semiconductor Co., Ltd.	11
Advanced Micro-Fabrication Equipment Inc. China	9
Huayi Microelectronics Co., Ltd.	9
Shaanxi Huajing Micro-Electronic Co., Ltd.	9
Jiangsu Nata Opto-electronic Material Co., Ltd.	8
TSMC	8
Applied Materials (China) Inc.	8

presents a summary of the out-degree scores of the top 10 companies This central position is reflected in their ranking among the top 10 in terms of out-degree, signifying their extensive collaborative engagements and resource exchanges with a wide array of downstream enterprises.

5.4.3. Company Betweenness Centrality

In this study, emphasis is placed on companies that rank among the top 10 in terms of betweenness centrality, due to their indispensable intermediary role within the network. This position demands intricate coordination and collaboration with a diverse set of stakeholders, including material suppliers, equipment manufacturers, and clients (electronic product manufacturers). Such an intermediary status underscores their pivotal role in orchestrating and regulating the flow of resources and information throughout the network.

The elevated betweenness centrality observed in these nodes implies that their removal or disruption could precipitate network fragmentation or disrupt the continuity of information flow. Functioning as critical conduits within the network, these nodes amass considerable resource information, facilitating the exchange of resources and information among other nodes. Their function mirrors that of a “broker” within the entirety of the constructed network, underscoring their integral role in maintaining network cohesion and operational fluidity.

The analysis of key players in industrial chain cooperation involved examining the betweenness centrality of each enterprise.

Table 4. The betweenness centrality of the top 10 enterprises.

Company	Betweenness Centrality
Shaanxi Semiconductor Pilot Technology Center Co., Ltd.	2832.14
Samsung Semiconductor (China) Co., Ltd.	2810.76
HT-tech	2789.98
Sanechips Technology Co., Ltd.	2718.56
Huayi Microelectronics Co., Ltd.	2578.22
SMIC	2503.49
Lonten Semiconductor Co., Ltd.	2239.71
TSMC	2178.95
CRS Technology Co., Ltd.	1990.77
Unigroup Guoxin Microelectronics Co., Ltd.	1738.70

presents a summary of the betweenness centrality scores of the top 10 companies, which serve as indicators of their significance within the industrial chain network to a certain degree. Nodes characterized by high betweenness centrality possess a measure of control over the interactions of resources within the network and exert substantial influence on its structural configuration. Furthermore, an analysis of degree centrality suggests a correlation, where nodes with an elevated betweenness centrality often exhibit a high degree centrality as well. This reveals that these top-ranking nodes are not only in contact with a multitude of enterprises but also hold significant sway over the interactions among these entities. Such findings highlight their indispensable core position within the intricate network of enterprises. Within the framework of the constructed complex network, these entities are deemed core businesses, reflecting their central and pivotal roles in influencing network dynamics and interactions.

5.4.4. Company Cluster Coefficient

The top 10 companies, as ranked by their clustering coefficient values, demonstrate a pronounced degree of clustering, primarily due to their extensive networks of affiliated companies. This clustering enables businesses within the group to engage in transactions at reduced costs, fostering a conducive environment for information resource sharing among them. Consequently, this arrangement facilitates heightened technical exchanges, elevated mutual participation, and the pursuit of shared strategic objectives among the companies. Such synergistic business activities not only complement one another but also enhance cooperation between enterprises, thereby driving growth within the cluster. Within a business cluster, collaboration is typically spearheaded by larger, core enterprises. Subsequent businesses join the cluster by strengthening their ties with these central entities. Consequently, these companies become influenced by the core enterprise regarding various aspects such as business operations, market strategies, technology, and distribution channels. This results in a dependency on the core company and interdependence among businesses within the cluster, highlighting the pivotal role of core enterprises in shaping the cluster’s dynamics and direction.

In these scenarios, the business activities of companies within the cluster are closely interlinked, particularly with the core enterprises that guide it. As shown in

Table 5. The clustering coefficient of the top 10 enterprises.

Company	Cluster Coefficient
Powertech Technology Inc.	0.3711
Infineon Technologies.	0.3682
Micron Technology (Xian)	0.3428
Shaanxi Electronic Core Industry Times Technology Co., Ltd.	0.3402
Huayi Microelectronics Co., Ltd.	0.3368
Samsung Semiconductor (China) Co., Ltd.	0.3347
BYD Electronics (Xi’an)	0.3271
CRS Technology Co., Ltd.	0.3239
HT-tech	0.3014
Lonten Semiconductor Co., Ltd.	0.2876

, the clustering coefficients of the top 10 companies in the industrial chain network are listed. The clustering coefficient is an indicator used to evaluate the closeness of connections between a company and its neighboring companies. A higher clustering coefficient signifies that a company has more triangular relationships within the network, indicating tighter connections among enterprises. Businesses within the cluster can leverage their partnerships to collaboratively address external risks, fostering a conducive atmosphere for innovation, resource sharing, and effective risk management. While this clustering effect engenders a supportive ecosystem, it simultaneously engenders a level of dependency that may influence the autonomy and adaptability of the individual companies constituting the cluster.

5.4.5. PCA Process for Research Documentation

The CICPI integrates several critical metrics, encompassing industry chain efficiency, resilience, and innovation capabilities, to furnish a holistic assessment of industry chain performance. To ensure the equitable and consistent integration and comparison of different components in calculating the comprehensive performance index, the study employs principal component analysis (PCA) for determining the weights of the three sub-indicators. The selection process involves identifying the most pertinent indicators to the industrial chain efficiency index (ICEI), industrial chain resilience index (ICRI), and industrial chain innovation capability index (ICICI), specifically: average path length and network density for the ICEI; average degree and standard deviation for the ICRI; and clustering coefficient and network density for the ICICI. These indicators form a dataset that encapsulates the key aspects of efficiency, resilience, and innovation capabilities within the industrial chain.

Table 6. The reason of selected variables.

Variables	Main Findings
Average Path Length	Represents the efficiency of information and resource transmission within the network.
Network Density	Indicates the overall connectedness and cohesiveness of the network.
Average Degree	Reflects the average number of connections per node, showing network robustness.
Standard Deviation	Captures the variability in connections, essential for understanding resilience.
Clustering Coefficient	Measures the degree to which nodes in a network cluster together, highlighting collaboration potential.
Network Density (Average)	Reinforces the importance of interconnectedness for innovation capacity.

shows the reasons for selecting these variables in this study. Through PCA, the study aims to distill these diverse indicators into a composite measure that accurately reflects the multifaceted performance of industry chains, thereby enabling a nuanced understanding of their operational dynamics.

Before constructing the PCA model, the data were normalized using the Z-score standardization method to ensure each variable contributes equally to the analysis. The Z-score standardization formula used is

$$Z=\frac{(X-\mu )}{\sigma }$$

(10)

where X is the original value, μ is the mean, and σ is the standard deviation.

The covariance matrix was computed from the normalized data to capture the variance and covariance between different variables. The study chooses six variables (average path length, network density, average degree, standard deviation, clustering coefficient, and network density), and the covariance matrix C would be as follows:

$$C=\left[\begin{array}{cccc}\mathrm{c}\mathrm{o}\mathrm{v}(X_1,X_1)& \mathrm{c}\mathrm{o}\mathrm{v}(X_1,X_2)& \cdots & \mathrm{c}\mathrm{o}\mathrm{v}(X_1,X_6)\\ \mathrm{c}\mathrm{o}\mathrm{v}(X_2,X_1)& \mathrm{c}\mathrm{o}\mathrm{v}(X_2,X_2)& \cdots & \mathrm{c}\mathrm{o}\mathrm{v}(X_2,X_6)\\ ⋮& ⋮& \ddots & ⋮\\ \mathrm{c}\mathrm{o}\mathrm{v}(X_6,X_1)& \mathrm{c}\mathrm{o}\mathrm{v}(X_6,X_2)& \cdots & \mathrm{c}\mathrm{o}\mathrm{v}(X_6,X_6)\end{array}\right]$$

(11)

The next step involves performing an eigenvalue decomposition of the covariance matrix to find the eigenvalues and eigenvectors. The eigenvalues indicate the amount of variance captured by each principal component, and the eigenvectors represent the direction of maximum variance in the data. Typically, the principal components are selected based on the explained variance. For this study, the principal components with the highest eigenvalues were chosen. The cumulative explained variance is calculated to ensure the selected components capture a significant portion of the total variance. The principal components (eigenvectors) are then used to transform the original data into a new set of uncorrelated variables (principal components). This transformation is performed by multiplying the eigenvectors with the normalized data matrix.

The first principal component (PC1) was found to capture a substantial portion of the variance, emphasizing the importance of average path length and network density in the ICEI. Similarly, PC2 highlighted the significance of average degree and standard deviation in the ICRI. The clustering coefficient and network density were pivotal in the ICICI. Given the following normalized data for three sample points with six variables,

$$\left[\begin{array}{cccccc}0.5& -0.1& 0.3& -0.4& 0.7& -0.5\\ -0.3& 0.2& -0.6& 0.1& -0.1& 0.3\\ 0.2& -0.1& 0.5& 0.2& 0.1& -0.3\end{array}\right]$$

The covariance matrix $C$ is computed as

$$C=\frac{1}{n-1}\sum _{i=1}^n(X_i-\overline{X}){(X_i-\overline{X})}^T$$

(12)

where n is the number of observations, X_i is each data point, and $\overline{X}$ is the mean of the data points.

By performing eigenvalue decomposition on the covariance matrix, we can determine the principal components and their associated eigenvalues. This process allows us to understand the underlying structure of the data and the contribution of each principal component to the overall variance. The weights obtained from the first principal component were normalized to ensure that their aggregate equals one, thus facilitating an intuitive representation of the relative significance of each indicator within the comprehensive index. Figure 4 illustrates the PCA covariance matrix, which helps in understanding the underlying structure of the data and the principal components that contribute most significantly to the variance.

5.4.6. Comprehensive Industry Chain Performance Index

According to the outcomes of the principal component analysis (PCA), the normalized weights assigned to the industry chain efficiency index (ICEI), industry chain resilience index (ICRI), and industry chain innovation capability index (ICICI) stood at approximately 0.43, 0.14, and 0.43, respectively. This allocation underscores the pronounced emphasis on both efficiency and innovation capabilities within the industry chain, attributing equal importance to these aspects, while resilience, though critical, is weighted less heavily in this specific analysis framework. Figure 5 shows the optimal weights derived from the analysis, highlighting the relative importance of each factor in the overall index calculation. This distribution reflects the analytical focus and priorities derived from PCA, highlighting the integral roles of efficiency and innovation in determining the overall performance of the industry chain. The allocation of weights in the comprehensive industry chain performance index (CICPI) suggests that the efficiency and innovation capability of the industry chain exert a more substantial influence on its overall performance, in contrast to the resilience index, which has a comparatively lesser impact. This weighting scheme underscores the critical importance of bolstering efficiency and fostering innovation within the industry chain. It advises businesses and policymakers to prioritize these areas for enhancement, without neglecting the resilience aspect of the industry chain. By doing so, they can ensure not only the chain’s continuous improvement and competitiveness but also its stability and capacity to recover from diverse challenges. This balanced approach enables a strategic focus on areas most impactful for growth while maintaining the resilience necessary to navigate and adapt to unforeseen circumstances.

By substituting the optimal weight value into the above Formula (9), the final value of the comprehensive industrial chain performance index (CICPI) of each enterprise can be obtained. As shown in

Table 7. The CICPI of the top 10 enterprises.

Company	CICPI
Samsung Semiconductor (China) Co., Ltd.	0.84352
HT-tech	0.80200
SMIC	0.79674
BYD Electronics (Xi’an)	0.78433
Applied Materials (Xi’an) Co., Ltd.	0.77921
Micron Semiconductor (Xi’an) Co., Ltd.	0.77201
Xi’an Xiangteng Micro-Electronic Technology Co., Ltd.	0.76851
Tsinghua Unigroup Co., Ltd.	0.75978
TSMC	0.75319
CRS Technology Co., Ltd.	0.74281

, the comprehensive industry chain performance index (CICPI) of the top 10 companies in the industry chain network is listed. The CICPI is a comprehensive indicator that takes into account a company’s efficiency, resilience, and innovation capabilities, with higher CICPI scores indicating superior performance in these areas. It can be observed that Samsung Semiconductor (China) Co., Ltd. has the highest CICPI, signifying an outstanding performance in efficiency, resilience, and innovation. These data demonstrate that these companies excel not only in individual metrics but also possess a strong overall competitiveness. These findings are significant for understanding the overall performance and relative importance of firms within the industry chain.

6. Discussion

This research leverages complex network theory alongside principal component analysis (PCA) to ascertain the weights of various indicators, facilitating a comprehensive evaluation of the industrial chain’s overall performance. This analytical approach enables the quantification and examination of critical nodes and subnetworks within the industrial chain, including prominent companies and centers of innovation. By integrating these methodologies, the study offers a nuanced understanding of the structural dynamics and performance drivers in the industrial chain, highlighting the pivotal roles played by key entities and their interrelations.

This study proposes the industrial chain efficiency index (ICEI), industrial chain resilience index (ICRI), and industrial chain innovation capability index (ICICI) as tools to measure industrial chain performance. Through detailed analysis of these indices, we are able to identify the performance of each enterprise in the industrial chain and provide corresponding management suggestions. In order to present the main findings and management insights more clearly, we summarize the main findings of each indicator and their management implications in

Table 8. Key findings and management insights.

The Main Indexes	Main Findings	Managerial Insights
ICEL	Core enterprises such as Samsung and HT-tech have the highest betweenness centrality in the network, showing their key roles in the flow of resources and information.	Core enterprises should strengthen cooperation with other enterprises, optimize resource allocation, and improve network collaboration efficiency and stability.
ICRL	The performance of local enterprises in efficiency and flexibility indicators is moderate, which is slightly insufficient compared with foreign-invested enterprises.	The automation and intelligent production technology of local enterprises should be improved, the agility of the supply chain should be enhanced, and internal management should be optimized.
ICICL	The insufficient innovation capabilities of local enterprises are mainly due to delayed adoption of new technologies and lack of innovative talents.	Increase investment in technology research and development, cultivate and attract innovative talents, break technological and policy bottlenecks, and promote technological renewal.

.

The research entails a detailed examination and comparison of the comprehensive industrial chain performance index (CICPI) against complex network metrics such as the node degree centrality, betweenness centrality, and closeness centrality. Prominent companies within the network, including Samsung Semiconductor, Hua Tian Technology, Xi’an Yi Si Wei, Applied Materials (Xi’an), BYD Electronics, Meguiar Semiconductor, Xi’an Microelectronics Technology Research Institute, Xi’an Purple Light Integrated Circuit Design Co., Ltd., Xi’an Changdian Technology Co., Ltd., and Shaanxi Huaxin Microelectronics Co., Ltd., demonstrate high scores across these metrics. This indicates that these entities not only engage in extensive interactions with other businesses but also exert considerable influence across the network, situating them as central figures within the entire industrial ecosystem. Typically positioned in the midstream and downstream segments of the industrial chain, these companies are distinguished by their advanced knowledge and technological capabilities. As such, the industrial revolution within the Shaanxi region is proposed to center around these key enterprises and their auxiliary partners, suggesting a strategic focus on leveraging their strengths to propel the region’s industrial development and innovation.

In evaluating the sub-indicators of the industrial chain efficiency index (ICEI), industrial chain resilience index (ICRI), and industrial chain innovation capability index (ICICI), it is noted that local Shaanxi enterprises typically perform at an average level in the ICEI and ICRI compared to foreign-funded enterprises and those that have migrated from other provinces. This indicates that local enterprises excel in leveraging automated and intelligent production technologies, maintaining efficient and agile supply chains, and implementing superior internal management practices, including process optimization, quality control, and cost management. However, the ICICI scores for local enterprises fall short when contrasted with foreign entities and those that have relocated from the eastern regions. This disparity may stem from various factors, such as delays in adopting new technologies or modernizing production processes, a scarcity of innovative talent or skilled workers, and technical or policy restrictions. One limitation of this study is its reliance on data from Shaanxi Province, which may not fully represent the national or global integrated circuit industry. In addition, static analysis does not capture dynamic changes in the industry, which may reduce the accuracy of the results.

7. Conclusions

This research centers on the integrated circuit enterprises in Shaanxi Province, employing sophisticated network analysis tools like Gephi to map out the province’s integrated circuit industry network. It meticulously identifies critical nodes within this network by leveraging pertinent complex network metrics. Furthermore, the study delves into the complex network analysis of Shaanxi’s integrated circuit industry chain, accentuating the utility of cutting-edge network theories and data analysis techniques. These methodologies are instrumental in uncovering the attributes of key nodes and understanding their consequential influence on the network’s overall performance. Through this analytical lens, the research provides insightful observations on the structural dynamics and operational efficiency of the integrated circuit industry in Shaanxi, highlighting the strategic roles of central enterprises and their interconnectivity within the industry ecosystem.

The initial findings of this study suggest that the integrated circuit industry chain in Shaanxi Province is predominantly anchored in midstream packaging and manufacturing enterprises. A significant portion of these enterprises relies on capital inflows and financial support from sources outside the province and internationally. The analysis uncovers vulnerabilities in terms of resilience and innovation within the industry, indicating that a cessation of external financial contributions or a shortfall in critical technologies could precipitate disruptions within the supply chain. Such vulnerabilities pose risks to the competitiveness of Shaanxi’s integrated circuit industry in both supply markets and technological innovation, potentially impeding the robust development of the entire industry chain. These insights underscore the necessity for strategic interventions aimed at bolstering innovation capabilities and resilience to ensure the sustainable growth of the integrated circuit industry in Shaanxi.

This study employs an innovative methodology that integrates complex network metrics with principal component analysis (PCA) to quantitatively evaluate the efficiency and resilience of the industrial chain. By adopting this approach, the research aims to provide fresh insights and practical analytical tools that could significantly benefit future investigations in related domains. This combination of methodologies promises to enhance the understanding of industrial chain dynamics, offering a nuanced perspective that could inform strategic decision-making and policy development.

The study conducted has some limitations. The data used in this study primarily come from the integrated circuit industry in Shaanxi Province. While these data provide a wealth of information for analysis, the results may not fully represent the national or global integrated circuit industry. Therefore, the generalizability of the study’s findings may be somewhat limited. Additionally, this study primarily relies on static network analysis and does not fully consider the impact of dynamic changes in the integrated circuit industry. Supply and industrial chains are inherently dynamic and constantly evolving over time. The failure to incorporate the temporal dimension may result in findings with limited explanatory power for the current environment.

To improve the generalizability of the research results, our future studies will expand the scope of data collection to include integrated circuit industry data from more regions or countries. Additionally, a comparative analysis based on cross-regional industry data will be conducted to enhance the comprehensiveness and representativeness of the results. Furthermore, a dynamic analysis model will be employed to consider temporal changes, studying the dynamic evolution of the supply chain and industrial chain across different periods. Through dynamic modeling, the evolution and development trends of the supply chain can be better understood and predicted.