Relevance Analysis of China’s Digital Industry

Abstract

Currently, the digital economy has emerged as a crucial force reshaping the global competitive landscape. This study aims to comprehensively explore the extent and economic significance of the digital industry. By utilizing existing national input–output tables, an input–output sequence table for the digital industry spanning from 2012 to 2020 was constructed. Through the application of input–output analysis and complex network methods, the study analyzed the interdependent effects of the digital industry and examined the structured characteristics of the industry network. The results indicate the following: (1) The core sectors of the digital industry primarily rely on the secondary industry as a foundation, utilizing its resources to drive their development. Simultaneously, these core sectors provide support to the tertiary industry, facilitating its transformation and upgrade. (2) The digital industry plays a role as a backward-linkage sector within the industrial chain, acting as an intermediate demand-driven industry that propels the transformation and growth of other industries. (3) China’s industrial network exhibits characteristics of both scale-free and small-world networks, featuring an uneven connectivity among industry nodes. (4) The digital foundational sectors are at the periphery of the network and have not developed a core advantage. The digital core sectors have not yet become the leading industries, but they have emerged as pivotal departments within the industry system, indicating the growing dominance of the digital industry in the overall economy.

1. Introduction

As a pivotal catalyst for fostering high-quality economic development [1], the digital economy has evolved into a “new engine” propelling economic growth, constantly giving birth to new industries, new models, and new formats [2]. It has assumed a critical role in fostering the growth of emerging industries, the upgrading of traditional industries, as well as in inclusive and sustainable development [3]. The digital economy exerts a profound and extensive influence on innovation and social progress [4,5,6,7].

According to calculations by Xian, Wang [8], the value added by core industries in the digital economy has risen from CNY 3.5825 trillion in 2012 to CNY 7.9637 trillion in 2020. From the data, we can see intuitively that the influence of the digital economy in the national economy increases annually, showing a trend of strong correlation and penetration.

Yu [9] discovered in their study that optimizing industrial linkages is fundamental to facilitating industrial transformation in China. Under the support of national policies, the digital economy industry has become an important driving force for optimizing industrial linkages. On the one hand, the industry can enhance its connection with the digital economy and its industry through digital transformation; on the other hand, it can break the communication barrier, promoting the integration and interaction between industries. Clearly, by developing the digital economy, we can efficiently optimize industrial linkages to achieve the goal of promoting industrial transformation [10,11] and strengthening the modern industrial system. Therefore, the promotion of digital economy development and its industries, the facilitation of integration between digital and traditional sectors, and the harnessing of the immense economic potential of the digital industry have become central concerns and areas of interest among scholars.

Based on this, this study aims to construct a national input–output table for the digital industry from 2012 to 2020, using data from the national input–output tables. It employs input–output analysis and complex network methods to analyze the interrelated effects of the digital industry, the overall structure of the national industry network, and the relative positions within it. It attempts to explain the industry relevance from the perspective of input–output relationships, clarify the interactions between traditional industries and digital industries, investigate the role played by the digital industry within the system, and take targeted measures to enhance the coverage of the digital economy, thereby promoting industrial transformation and development. This is of significant practical significance in fostering the facilitating industrial transformation and driving the realization of a “Digital China”.

The structure of this article is as follows: Section 2 mainly elucidates the relevant literature. Section 3 introduces the methods used in this study. Section 4 describes the compilation of the input–output sequence for the digital industry. Section 5 and Section 6 discuss the individual correlation effect of the digital industry and the overall structural effects of China’s industrial system. The final section presents the conclusion.

2. Literature Review

Currently, research on the digital economy is primarily focused on two aspects. The first is measuring the development of the digital economy. Initially, researchers focused on scrutinizing and summarizing the accounting studies of international organizations to provide ideas, frameworks, and relevant suggestions for measuring the development scale of the digital economy [12,13]. Subsequently, attention shifted toward the statistical characteristics of digital economic development [14]. More scholars are now conducting quantitative research on the digital economy, such as developing indicator systems [15] or compiling input–output tables [16,17] to assess the development of China’s digital economy.

The second aspect is that, with China’s economy entering a new normal and the rapid growth of the digital economy, the digital industry emerges. Many scholars have started exploring the impact of the digital industry on other industries and the national economy. From existing research, although the digital industry is not the leading or core industry of China’s economy [18], there are significant regional disparities in its development level [19]. However, it plays a crucial role in driving the development of the domestic economy, with substantial development potential and room for growth [20,21].

Many scholars have argued for the importance of the digital economy and its industries on the national economy from different perspectives. However, few studies have explored the role that the digital industry plays within the industrial system or how it promotes the development of the national economy through industrial relevance. To fill this gap, this paper attempts to explore, from the perspective of industrial relevance, how the digital industry supports industrial transformation and its role in the upgrading of industries.

To address this question, this paper needs to explore the linkages between different industrial sectors. Input–output analysis [22,23], pioneered by the American economist Wassily Leontief in 1936, is a classical and mature technique for industrial linkages research. It utilizes input–output tables and mathematical models to analyze the economic connections between different sectors, serving as a powerful tool for comprehensive economic analysis. Numerous scholars [24,25,26,27] have utilized input–output analysis to study the development of various industries and analyze their roles in the national economy. It is a vital method for revealing the internal mechanisms of industrial linkages.

However, input–output analysis primarily emphasizes the correlation effect of individuals and fails to consider the overall structural effects of the industrial system. To tackle this issue, Campbell introduced the concepts and methods of Graph Theory. By utilizing complex networks to analyze industrial linkages, Campbell depicted the connections of industries as a network and expand the scope of structural analysis, which helped to intuitively see the economic correlation of industries. In recent years, a large number of researchers have applied complex network theory to study the structural characteristics of industrial networks [28]. They have studied the overall structure features such as degree distribution, centrality, and clustering [29,30,31,32,33], explored the development trends, patterns, and stage positioning of different industries, as well as identified the key nodes within the industrial systems from a network perspective and delineate the propagation paths of industrial chain [34,35].

The application of complex network analysis to explore the characteristics of industrial networks has become a recent subject in this field. However, most of the existing literature only focus on horizontal comparisons of industrial linkages and hinder dynamic analysis of the evolutionary patterns of industrial structures. The main reason is that input–output tables, which are crucial to input–output analysis and serve as the basis for constructing industry linkage networks, are compiled with intervals. Due to the lack of continuity and timeliness in China’s input–output tables, it becomes challenging to analyze the changes characteristics of industrial structures.

To address this issue, researchers in academia have extensively studied the development of sequential input–output tables [36]. Currently, the RAS method is the primary approach used for compiling input–output tables [37], including both the standard RAS method and the improved RAS method [38]. In an empirical test conducted by Temurshoev et al. [39] comparing eight methods for updating input–output tables, it was found that the RAS method (specifically the GRAS method) outperformed other methods in terms of estimation accuracy. Therefore, this study adopts the official compilation method for extending tables and utilizes the RAS method to compile input–output tables for unknown years. Additionally, it constructs a digital industry input–output table to conduct a longitudinal analysis of the linkage and spillover effects within the digital industry. This approach facilitates a dynamic understanding of the characteristics of China’s industrial network structure, as well as the trends in development and changes in roles within the digital industry.

3. Theoretical Models and Methodologies

3.1. Input–Output Analysis Method

Input–output analysis organizes the national economy into a finite number of sectors, simplifying complex economic activities through the application of linear algebra. It relies on several assumptions, including (1) homogeneity, (2) direct consumption coefficients remain stable over a certain period, and (3) proportionality. Leontief developed a linkage model that connects the total demand, final demand, and intermediate demand in input–output tables:

$$AX+Y=X$$

$$X={(I-A)}^{-1}Y$$

The model reveals the relationship between final use (final demand) and total output (total demand), with the $(I-A)$ matrix being the core and foundation of the input–output model (the A represents the matrix of direct consumption coefficient).

$$I-A=\left(\begin{array}{ccc}1-a_{11}& \cdots & -a_{1n}\\ ⋮& \ddots & ⋮\\ -a_{n1}& \cdots & 1-a_{nn}\end{array}\right)$$

Viewed vertically, the elements of $(I-A)$ reflect the relationship between input and output. Negative represents input, while the elements on the main diagonal indicate the net output obtained after deducting self consumption. The introduction of $(I-A)$ enables simple mathematical models to explore complex economic networks, opening ways for analyzing the economy.

This article employs input–output analysis and relies on the constructed input–output sequence table specific to the digital industry as the fundamental data source for investigating the linkage effects within this sector. To explore the effects associated with the digital industry, a range of indicators including the total consumption coefficient, total distribution coefficient, influence coefficient, and sensitivity coefficient have been carefully selected. These indicators will shed light on the interconnected effects of the digital industry and provide valuable insights.

3.1.1. Total Consumption Coefficient

The total consumption coefficient quantifies the overall amount of resources consumed (the sum of direct and indirect consumption) from other industry sectors when a specific industry sector produces one unit of final product.

$$a_{ij}=\frac{x_{ij}}{x_j}{a}_{ij}\in A$$

$$B=A+A^2+\dots +A^{k}B={(I-A)}^{-1}-I$$

3.1.2. Total Distribution Coefficient

The total distribution coefficient denotes the comprehensive allocation of resources from other industry sectors when a specific industry sector initially invests one unit of product.

$$r_{ij}=\frac{x_{ij}}{x_j}{r}_{ij}\in R$$

$$K={(I-R)}^{-1}-I$$

The total consumption coefficient provides insights into the overall demand of the digital industry for resources from other sectors, allowing for an assessment of the digital industry’s level of dependence on different sectors. On the other hand, the total distribution coefficient reveals how resources are allocated within the digital industry, facilitating an analysis of the degree of interconnection between the digital industry and other sectors from a supply perspective.

3.1.3. Influence Coefficient and Sensitivity Coefficient

The influence coefficient $F_j$ quantifies the impact of a one-unit increase in final usage in sector j on the demand of all sectors in the national economy. On the other hand, the sensitivity coefficient indicates the level of responsiveness of sector i to a one-unit increase in final usage by all sectors in the national economy.

$$F_j=\frac{{\sum }_{i=1}^n{b}_{ij}}{\frac{1}{n}{\sum }_{i=1}^n{\sum }_{j=1}^n{b}_{ij}}(i,j=1,2,\dots \dots n)$$

$$G_i=\frac{{\sum }_{j=1}^n{b}_{ij}}{\frac{1}{n}{\sum }_{i=1}^n{\sum }_{j=1}^n{b}_{ij}}(i,j=1,2,\dots \dots n)$$

The influence coefficient and sensitivity coefficient provide insights into the impact and contribution of the digital industry to the national economy. If the influence coefficient (sensitivity coefficient) of a digital industry sector exceeds 1, it signifies that the sector’s ripple effect (sensitivity) is greater than the societal average level, indicating a higher degree of influence or responsiveness compared to other sectors in the economy.

3.2. Complex Network Analysis Methods

A complex system can be represented as a complex network, where the system’s elements are treated as nodes in the network, and the interrelationships between the elements are depicted as edges. The nature of the edges, such as being directed or undirected, weighted or unweighted, can be chosen based on the specific research question. In this study, we construct a directed and unweighted industry linkage network. To analyze the structural characteristics of China’s industry linkage network, various indicators from complex network analysis are utilized, including network density, small-worldness, scale-free properties, node degree, and eigenvector centrality. These indicators provide valuable insights into the properties and dynamics of China’s industry linkage network.

3.2.1. Network Density

Network density is a measure that quantifies the proportion of actual edges present in a network compared to the maximum number of possible edges as defined by its theoretical framework.

$$d\left(G\right)=\frac{L}{N(N-1)}$$

Network density serves as a metric to assess the degree of interconnectedness and stability within an industry network. A higher network density implies a stronger interlinkage among various industries, leading to a more stable overall network structure.

3.2.2. Scale-Free Property and Small-World Property

Scale-free properties and small-worldness are essential characteristics of complex networks. Scale-free properties are defined by the degree distribution following a power-law distribution, indicating that some nodes in the network have significantly higher degrees than others. Networks with scale-free properties exhibit an imbalanced distribution of nodes, and targeting a few highly connected nodes can result in network collapse. In the context of an industry network, the growth rate of industries associated with these highly connected nodes has a substantial impact on the overall development of the entire industrial system.

Networks with small-world properties enable the connection of initially disconnected nodes within a few intermediate steps. This characteristic is measured by high clustering coefficients and short average path lengths. The clustering coefficient indicates the degree of interconnectivity among neighboring nodes of a specific node in the network.

$$C=\frac{1}{N}\sum \frac{{\sum }_{b,a}{w}_{cb}{w}_{ba}{w}_{ca}}{max\left(W_{cb}\right){\sum }_{b,a}{w}_{bs}{w}_{sr}}$$

The average path length refers to the shortest number of steps of directed paths for all possible node pairs in the network.

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

Due to the inherent sensitivity of small-world networks, any interference with different nodes can swiftly propagate to neighboring nodes, thereby exerting a significant impact on the entire industry network.

3.2.3. Node Degree

The node degree refers to the number of edges connecting a node to other nodes. In a directed network, the node degree represents the sum of the outdegree and indegree of a node. In this study, outdegree refers to the number of intermediate input industries in the upstream sector, while indegree refers to the number of recipient industries in the downstream sector that receive inputs from the intermediate industries. Industries with higher node degrees indicate a central position in the network and close connections with other industries. When these industries experience fluctuations, the impact will spread to a greater number of industry sectors.

$$K_a^{out}={\sum }_b{x}_{ab}{K}_a^{in}={\sum }_b{x}_{ba}$$

$$K_a=K_a^{out}+K_a^{in}$$

3.2.4. Eigenvector Centrality

The eigenvector centrality is a metric used to assess the significance of a node by considering its connections to influential nodes within the network.

$$EC\left(a\right)=\frac{1}{\lambda }{\sum }_{b=a}^n{A}_{ab}{e}_b$$

Eigenvector centrality measures the importance of an industry by considering the importance of its connected industries, thereby emphasizing the industry’s value within the industrial network.

4. The Compilation of the Input–Output Sequence for the Digital Industry

Currently, there is a limited amount of literature on the compilation of input–output tables for the digital industry. Most studies have built upon the methods proposed by He [40], Zeng [41], and others to enhance the compilation of input–output tables for the information industry. However, a continuous type of input–output table for the digital industry has not been established yet. In this study, we utilized the national input–output tables published by the National Bureau of Statistics for the years 2012, 2015, 2017, 2018, and 2020 [42] and extensively utilized official data from sources such as the “China Statistical Yearbook [43]”, the “China Economic Census Yearbook [44]”, and the “China Culture and Related Industries Yearbook [45]”. Based on this data, we compiled a sequential input–output table for the Chinese digital industry, covering the period from 2012 to 2020.

4.1. Compiling the Input–Output Sequence Table

Input–output tables provide a comprehensive representation of the structural characteristics of the national economy and enable systematic quantitative analysis of interrelationships between different sectors. In China, these tables are typically published intermittently, resulting in a lack of continuity. To establish a sequential input–output table for the digital industry, it is necessary to compile a series of such tables. This study is based on published statistical data and existing input–output tables. The RAS (Rasch model with Additive and Synergetic effects) method is utilized to construct the national input–output table for the unknown year, thereby creating a sequence of input–output tables spanning from 2012 to 2020. The RAS method, also known as the double proportional scaling method, iteratively adjusts the existing matrix A by considering row and column sums, ultimately generating a “new” matrix X that satisfies the specified row sum u and column sum v. This method is known for its practicality and high estimation accuracy. The compilation process outlined in this section involves three steps: computing the initial input matrix, calculating the final demand matrix, and determining the intermediate flow matrix.

4.1.1. Sector Classification of the Input–Output Table

Taking into account the inconsistent sector classification in the existing input–output tables for different years, this study adopts the “National Economic Industry Classification (GB/T 4754-2017) [46]” and incorporates the detailed sector classification provided by the National Bureau of Statistics in the known-year input–output tables. Consequently, the sectors that differ across the years 2012, 2015, 2017, 2018, and 2020 are consolidated or divided to establish a consistent 42-sector classification for the input–output tables. The classification of the 42 sectors is presented in

Table 1. Forty-two industries classification.

No.	Industrial Sector	No.	Industrial Sector
01	Agricultural, forestry, animal husbandry and fishery products and services	22	Other manufactured products
02	Coal mining products	23	Waste and scrap
03	Oil and gas extraction products	24	Metal products, machinery and equipment repair services
04	Metal mining products	25	Electricity, heat production and supply
05	Non-metallic and other ore mining products	26	Gas production and supply
06	Food and tobacco	27	Water production and supply
07	Textile	28	Construction
08	Textile, clothing, shoes, hats, leather, down and other products	29	Wholesale and retail
09	Wood processing and furniture	30	Transportation, warehousing and postal
10	Paper printing and cultural, educational, and sports goods	31	Accommodation and catering
11	Petroleum, coking products and processed nuclear fuel products	32	Information transmission, software and information technology services
12	Chemical products	33	Finance
13	Non-metallic mineral products	34	Real estate
14	Metal smelting and rolling products	35	Leasing and business services
15	Metal products	36	Scientific research and technical services
16	General equipment	37	Water, environment and public facilities management
17	specialized equipment	38	Residential services, repairs and other services
18	Transportation equipment	39	Education
19	Electrical machinery and equipment	40	Health and social work
20	Communication equipment, computers and other electronic equipment	41	Culture, sports and entertainment
21	Instruments and meters	42	Public administration, social security and organization

.

4.1.2. Explanation of the Compilation Method

In this section, we present an overview of the framework used to compile the input–output table sequence. To illustrate the process, we will focus on the compilation of the 2013 input–output table. The first step involves gathering data from statistical yearbooks for the year 2013, including income-based value-added and its sub-items such as labor compensation, depreciation of fixed assets, net production taxes, and operating surplus. These data are then used to calculate the row sums for the initial input matrix. However, for certain sectors (e.g., sectors 02–19), the value-added data are unavailable. In such cases, the target-year value-added ratio matrix is estimated using the corresponding value-added ratio matrix from 2012. With the value-added data from 2013 and the estimated value-added ratios, the sector value-added matrix for 2013 is calculated.

$$v_j^{2013}=v^{2013}{a}_j^{2013}$$

$$a_j^{2013}=a_j^{2012}\theta$$

where $v_j^{2013}$ represents the value added of sector j in 2013, $v^{2013}$ represents the total value added of all sectors in 2013, $a_j^{2013}$ represents the proportion of sector j’s value added to the total value added of all sectors in 2013, and $\theta$ represents the growth rate of value-added ratios from 2012 to 2013, which can be calculated based on the average annual growth rate from 2012 to 2015. With this information, we can calculate the row and column sums of the initial input matrix and utilize the RAS method to derive the initial input matrix for 2013.

The second step involves estimating the target-year value-added ratios by referring to the input–output tables of known years. This estimation allows us to infer the total output of each sector for the target year as a control indicator.

In the third step, data on consumption expenditure, gross capital formation, total imports, total exports, and other factors are obtained from the National Bureau of Statistics. Similar to the previous step, we estimate the row sums of the final demand matrix for the target year and calculate the final demand matrix.

The fourth step focuses on ensuring consistency between the initial input matrix and the final demand matrix. In this study, we use the input-based GDP of the initial input matrix as a reference to adjust the final demand matrix.

The fifth step involves calculating the intermediate flow matrix. By subtracting the expenditure-based value-added data and income-based value-added data from the total output data, we obtain the total intermediate use vector and the total intermediate input vector. The RAS method is then employed to compute the intermediate flow matrix.

Finally, the initial input matrix, final demand matrix, and intermediate flow matrix are combined to generate the national input–output table for the target year, consisting of 42 sectors. Throughout the compilation process, maintaining overall balance is crucial. After examination, the input–output tables for 2013, 2014, 2016, and 2019 are confirmed to maintain balance.

4.2. Compilation of the Input–Output Sequence Table for the Digital Industry

4.2.1. Definition and Classification of the Digital Industry

In June 2021, the National Bureau of Statistics released the ”Statistical Classification of the Digital Economy and Its Core Industries (2021) [47]”, providing a clear definition of the fundamental scope of the digital economy industry. This classification categorizes the digital economy into five main sectors: digital product manufacturing, digital product services, digital technology applications, digital factor-driven industries, and digital efficiency enhancement industries. By offering a unified statistical framework and scope, this classification facilitates the measurement of China’s digital economy. In this study, we will leverage this statistical classification to construct a national input–output table specifically for the Chinese digital industry.

To compile the input–output table for the digital industry, the first step involves aligning the 42 sectors in the input–output table with the digital industry. In this study, we adopt the “Classification of Digital Economy and its Core Industries (2021)”, published by the National Bureau of Statistics as the standard. By combining this classification with the 42-sector classification, we identify two digital core sectors, thirteen digital foundational sectors, and twenty-seven traditional industry sectors.

It is important to note that, due to data availability, this study focuses solely on the digital core industries outlined in the “Classification of Digital Economy and its Core Industries (2021)” for constructing the digital input–output table. These core industries encompass digital product manufacturing, digital product services, digital technology application, and digital factor-driven industries. The digital core sectors directly correspond to specific industries associated with digital technology, namely, communication equipment, computers, and other electronic equipment, as well as information transmission, software, and information technology services.

The digital foundational sectors encompass products or services that emerge from the deep integration of traditional industries and digital technology. They include elements of traditional industries as well as new models and formats resulting from the penetration of digital technology into these industries. In the input–output table, the digital components considered for the following thirteen sectors are: paper printing and cultural, educational, and sports goods; chemical products; general equipment; specialized equipment; electrical machinery and equipment; instruments and meters; construction; wholesale and retail; finance; leasing and business services; scientific research and technical services; residential services, repair, and other services; and culture, sports, and entertainment.

4.2.2. Explanation of the Compilation Method

The key to compiling the input–output table for the digital economy lies in effectively separating and integrating digital economic activities from traditional national economic activities within the national input–output table. The digital core sectors, including communication equipment, computers, and other electronic devices, as well as information transmission, software, and information technology services, constitute a distinct sector within the digital industry, allowing for direct consolidation.

Regarding the 13 industry sectors classified under the digital foundational sectors, this study utilizes the proportion of digital economic revenue to total revenue in each industry as separation coefficients. These coefficients are based on data from the “China Economic Census Yearbook” for 2013 and 2018. They serve as a basis for separating the digital foundational sectors in those respective years. By using these separation coefficients as a reference, it becomes possible to estimate the separation coefficients for unknown years within the digital foundational sectors.

Furthermore, in cases where revenue data for certain subcategories such as digital content publishing and internet finance are unavailable, this study calculates their separation coefficients based on the proportion of sales amount or employment.

Table 2. Separation coefficients of the digital industry.

No.	Industrial Sector	Separation Coefficients in 2018
10	Paper printing and cultural, educational, and sports goods	0.0058
12	Chemical products	0.0068
16	General equipment	0.0261
17	Specialized equipment	0.0210
19	Electrical machinery and equipment	0.2990
21	Instruments and meters	0.3607
28	Construction	0.1002
29	Wholesale and retail	0.0471
33	Finance	0.3315
35	Leasing and business services	0.0147
36	Scientific research and technical services	0.0941
38	Residential services, repairs, and other services	0.0559
41	Culture, sports, and entertainment	0.0068

presents the separation coefficients for the 13 digital foundational sectors in 2018.

Based on the obtained sector separation coefficients $\alpha$, the aforementioned digital foundational sector j is divided into two parts, with $(1-\alpha )x_j$ representing the original traditional industry sector and $\alpha x_j$ representing the digital foundational sector. Using the aforementioned method, the input–output tables for the digital industry from 2012 to 2020 are compiled.

The basic format of the input–output table for the digital industry, as compiled in this study, is presented in

Table 3. Basic format of the input–output table for the digital industry.

	Output	Intermediate Demand			Final Demand				Import	Total Output
Input		40 Traditional Sectors	Digital Core Sector	Digital Foundational Sector	Household Consumption Expenditure	Government Consumption Expenditure	Gross Capital Formation	Export
Intermediate input	40 traditional sectors	Intermediate flow matrix			Final demand matrix
	Digital core sector
	Digital foundational sector
Initial input	Labor compensation	Initial input matrix
	Net production taxes
	Depreciation of fixed assets
	Operating surplus
Total input

. It consists of a total of 42 sectors, with the first 40 sectors representing traditional sectors of the national economy, the 41st sector representing the digital core sector, and the 42nd sector representing the digital foundational sector.

5. Input–Output Analysis of the Digital Industry

Based on the previously mentioned input–output tables for the digital industry constructed from 2012 to 2020, conducting an input–output analysis of the digital industry enables us to examine the interrelationships and positioning of the digital industry within the sectors of the national economy.

5.1. Analysis of Interdependent Effects in the Digital Industry

In general, if an industry B in an industrial chain develops rapidly, it will exert a positive impact on other directly related industries through industrial interdependent effects. For example, it will provide more supply to downstream industry C, thereby stimulating its development. At the same time, there will be a significant increase in demand for raw materials in upstream industry A, consequently fostering its development. Their development, in turn, further promotes the growth of industry B, forming interaction between industries, as illustrated in Figure 1. This study aims to analyze the backward and forward linkages of the digital industry within the industry chain by computing the coefficients of total consumption and total distribution.

5.1.1. Analysis of Backward Full Linkage Effect

During the production process, the digital industry relies on various production factors from other sectors. Analyzing the backward linkage effects of the digital industry enables us to understand the extent of its dependence on upstream industries and its role in driving socio-economic activities. The backward linkage effects of the digital industry are quantified using the coefficients of total consumption.

Based on the data from the input–output tables for the digital industry spanning from 2012 to 2020, separate calculations were performed for the digital core sector and the digital foundational sector. The findings are presented in

Table 4. Total consumption coefficient of the digital core sector from 2012 to 2020.

	2012	2013	2014	2015	2016	2017	2018	2019	2020
Digital core sector	0.494	0.093	0.720	0.678	0.682	0.691	0.693	0.726	0.672
Chemical products	0.301	0.259	0.251	0.236	0.198	0.151	0.140	0.139	0.120
metal smelting and rolling processing products	0.250	0.253	0.228	0.223	0.190	0.160	0.153	0.162	0.137
Electrical machinery and equipment	0.073	0.098	0.095	0.092	0.086	0.078	0.074	0.079	0.067
Electricity, heat production and supply	0.103	0.087	0.084	0.094	0.075	0.066	0.066	0.065	0.063
Wholesale and retail	0.097	0.102	0.109	0.111	0.119	0.097	0.102	0.108	0.103
Transportation, warehousing and postal	0.091	0.093	0.096	0.097	0.082	0.083	0.086	0.075	0.081
Finance	0.096	0.095	0.090	0.095	0.089	0.059	0.055	0.056	0.047
Real estate	0.021	0.024	0.025	0.032	0.035	0.050	0.054	0.056	0.072
Leasing and business services	0.071	0.081	0.089	0.099	0.108	0.099	0.106	0.122	0.121
paper printing and cultural, educational, and sports goods	0.152	0.056	0.056	0.059	0.052	0.047	0.047	0.049	0.052
Food and tobacco	0.050	0.054	0.059	0.063	0.048	0.041	0.039	0.041	0.039
Agricultural, forestry, animal husbandry and fishery products and services	0.077	0.050	0.054	0.060	0.046	0.035	0.034	0.035	0.037

and

Table 5. Total consumption coefficient of the digital foundational sector from 2012 to 2020.

	2012	2013	2014	2015	2016	2017	2018	2019	2020
Digital core sector	0.093	0.116	0.118	0.111	0.106	0.104	0.112	0.103	0.099
Chemical products	0.183	0.178	0.170	0.154	0.121	0.106	0.094	0.084	0.070
Non-metallic mineral products	0.198	0.177	0.159	0.141	0.115	0.103	0.095	0.085	0.072
metal smelting and rolling processing products	0.289	0.256	0.221	0.173	0.139	0.116	0.108	0.100	0.086
Electricity, heat production and supply	0.103	0.088	0.083	0.082	0.062	0.054	0.052	0.046	0.044
Wholesale and retail	0.063	0.066	0.071	0.070	0.071	0.065	0.067	0.063	0.057
Transportation, warehousing and postal	0.094	0.098	0.101	0.100	0.083	0.081	0.080	0.063	0.064
Finance	0.095	0.092	0.088	0.098	0.095	0.084	0.078	0.070	0.060
Real estate	0.028	0.035	0.038	0.048	0.059	0.073	0.078	0.074	0.070
Leasing and business services	0.066	0.081	0.092	0.097	0.111	0.108	0.114	0.118	0.098
digital foundational sector	0.010	0.016	0.023	0.030	0.037	0.040	0.046	0.050	0.052
Metal products	0.064	0.062	0.059	0.055	0.047	0.042	0.040	0.037	0.032
Agricultural, forestry, animal husbandry and fishery products and services	0.051	0.052	0.055	0.058	0.047	0.039	0.036	0.033	0.031

(due to space constraints, this study only includes the top ten sectors closely associated with the digital industry for each year, and the same format is followed in subsequent tables).

From Table 4, it can be observed that the five major sectors closely associated with the digital core sector are the manufacturing of electronic components, chemical products, metal smelting and processing, leasing and business services, and wholesale and retail. These sectors serve as the primary intermediate input sectors for the digital core sector. The digital core sector exhibits the highest consumption of its own output, indicating that its development primarily relies on the growth of its core technology. Additionally, apart from its own consumption, the digital core sector relies heavily on inputs from the secondary industry. This highlights the inseparable connection between the development of the digital economy and the support of the manufacturing industry, signifying that the rapid advancement of the digital industry will further propel innovation and upgrades in the manufacturing industry.

From a temporal perspective, the consumption of the digital core sector has consistently maintained a relatively high level. Furthermore, with the integration and development of digital technology and traditional industries, sectors such as real estate, wholesale and retail, leasing and business services, and other tertiary industries exhibit a continuous growth trend in their contributions to the digital core sector.

For the digital foundational sector, it exhibits significant backward linkages with the digital core sector, chemical products, non-metallic mineral products, metal smelting and rolling processing products, leasing, and business services. The digital foundational sector relies heavily on the digital core sector due to its primary reliance on digital technology for development. As for its self-reliance, it is relatively low. Like the digital core sectors, manufacturing industries such as chemical products, non-metallic mineral products, metal smelting, and rolling processing products also contribute significantly to the development of the digital foundational sector. However, starting in 2018, the intermediate input from the tertiary industry to the digital foundational sector has surpassed that from the secondary industry.

Overall, the upstream sectors of the digital industry are mainly concentrated in the manufacturing industry. However, China’s manufacturing industry has been operating under a high-input, high-consumption production model, which puts tremendous pressure on resources and the environment. While the development of the digital industry has a strong dependence on traditional manufacturing sectors such as energy, electricity, and materials, the level of development in these sectors directly influences the progress of the digital industry. Nevertheless, the flourishing growth of the digital industry in the era of digitalization will also compel the manufacturing industry to embrace digital transformation and innovation. By improving technological capabilities, it enables sustainable development and optimizes China’s industrial structure.

5.1.2. Analysis of Forward Full Linkage Effect

In contrast to backward linkages, forward linkages refer to the digital industry’s provision of intermediate inputs to downstream industries as an upstream industry, showcasing the digital industry’s role in driving the development of these downstream sectors. The forward linkage effects of the digital industry can be quantified using the coefficients of total distribution.

Examining

Table 6. Total distribution coefficient of the digital core sector from 2012 to 2020.

	2012	2013	2014	2015	2016	2017	2018	2019	2020
Chemical products	0.090	0.102	0.103	0.098	0.080	0.059	0.054	0.055	0.045
Digital core sector	0.677	0.727	0.719	0.678	0.682	0.691	0.693	0.726	0.672
General equipment	0.087	0.100	0.100	0.093	0.078	0.060	0.052	0.057	0.048
Specialized equipment	0.055	0.060	0.057	0.052	0.048	0.044	0.040	0.045	0.039
Transportation equipment	0.092	0.104	0.103	0.100	0.093	0.079	0.073	0.075	0.063
Electrical machinery and equipment	0.082	0.094	0.094	0.086	0.078	0.069	0.064	0.071	0.062
Construction	0.125	0.150	0.170	0.181	0.179	0.145	0.153	0.158	0.146
Leasing and business services	0.050	0.062	0.070	0.072	0.076	0.048	0.052	0.059	0.051
Scientific research and technical services	0.051	0.060	0.062	0.055	0.061	0.058	0.062	0.059	0.067
Metal smelting and processing products	0.067	0.081	0.084	0.081	0.058	0.034	0.032	0.035	0.029
Electricity, heat production and supply	0.056	0.064	0.065	0.065	0.052	0.044	0.045	0.049	0.043
Transportation, warehousing and postal	0.040	0.046	0.047	0.046	0.039	0.051	0.056	0.052	0.063
Public administration, social security and organization	0.025	0.026	0.026	0.027	0.033	0.034	0.047	0.049	0.049

, we can observe that the digital core sector, construction, transportation equipment, and general equipment are the key industries with significant forward linkages to the digital core sector. Among them, the digital core sector exhibits the highest degree of self-input, as a substantial portion of its produced goods and services are reinvested within the sector itself. Sectors such as construction, transportation equipment, leasing, and business services generate substantial demand and consumption for the digital core sector, relying on it for support and further growth. Over time, the reliance of the secondary industries, including chemical products, general equipment, and specialized equipment, on the digital core sectors has gradually declined, while the dependence of the tertiary industries, encompassing construction, transportation, warehousing, and postal services, on the digital core sectors has gradually increased. Now, with the advancement of digital technology, the integration between the digital industry and the service sector enables the service industry to quickly respond to market demands, ensuring that services truly meet customer needs and facilitating the upgrading of the service industry.

As shown in

Table 7. Total distribution coefficient of the digital foundational sector from 2012 to 2020.

	2012	2013	2014	2015	2016	2017	2018	2019	2020
Digital core sector	0.054	0.075	0.089	0.102	0.107	0.095	0.100	0.108	0.116
Digital foundational sector	0.010	0.016	0.023	0.030	0.037	0.040	0.046	0.050	0.052
Chemical products	0.050	0.074	0.089	0.104	0.098	0.077	0.073	0.079	0.071
Non-metallic mineral products	0.019	0.031	0.040	0.050	0.046	0.036	0.035	0.038	0.034
Metal smelting and processing Products	0.045	0.071	0.087	0.102	0.086	0.059	0.058	0.064	0.058
Transportation equipment	0.031	0.043	0.050	0.057	0.057	0.047	0.044	0.046	0.043
Construction	0.069	0.101	0.132	0.152	0.165	0.149	0.156	0.166	0.161
Wholesale and retail	0.022	0.034	0.045	0.053	0.055	0.054	0.060	0.067	0.068
Transportation, warehousing and postal	0.035	0.051	0.061	0.072	0.069	0.094	0.086	0.085	0.099
Finance	0.023	0.030	0.032	0.040	0.049	0.050	0.049	0.044	0.038
Real estate	0.021	0.031	0.037	0.042	0.048	0.060	0.066	0.068	0.077
Leasing and business services	0.019	0.030	0.040	0.051	0.061	0.058	0.061	0.071	0.070
Food and tobacco	0.028	0.037	0.042	0.043	0.049	0.047	0.039	0.043	0.039
Electricity, heat production and supply	0.023	0.035	0.045	0.056	0.049	0.037	0.039	0.043	0.042

, it is evident that the digital foundational sector, as an emerging industry sector, has not significantly supported other sectors of the national economy. Nevertheless, during the study period, most sectors have demonstrated varying degrees of increased dependence on the digital foundational sector. Notably, sectors such as transportation, warehousing, and postal services, construction, leasing, and business services have experienced reliance growth exceeding 100%.

In summary, the digital industry plays an increasingly significant role in sectors such as transportation, warehousing, and postal services, construction, leasing, and business services, establishing tighter connections with these sectors. At the same time, by comparing the backward linkages, we can observe that the digital core sector primarily utilizes the secondary industry as a foundation, consuming its resources to fuel its development. Simultaneously, the digital core sector acts as a support for the tertiary industry, driving its transformation and upgrading. Leveraging the digital core sector as a “bridge” and harnessing the mechanism of industry linkages, on the one hand, can enhance the sectors’ reliance on the digital industry, leading to a broader coverage of the digital economy. On the other hand, it can foster the rejuvenation and advancement of industries closely linked to the digital industry, thus expediting the progress of supply-side structural reforms.

5.2. Analysis of Spillover Effects in the Digital Industry

In the industrial network, the production and business activities of the digital industry have a direct or indirect impact on other sectors, thus influencing the overall economic environment. Analyzing the ripple effects of industry sectors can provide insights into their role and position in the national economy. This study will examine the ripple effects of the digital industry from two perspectives: the influence coefficient and the responsiveness coefficient.

5.2.1. Influence Analysis

Overall, during the period of 2012 to 2020, there were a total of 25 sectors with influence coefficients greater than 1. The majority of these sectors were concentrated in high-tech industries, including electrical machinery and equipment, general equipment, and specialized equipment. These industries are characterized by high technological content and value added. Their development has the potential to stimulate the competitive growth of other sectors, thereby driving the industrial structure towards a knowledge-intensive direction.

Specifically, within the digital core sector, the influence coefficients from 2012 to 2020 were consistently greater than 1, surpassing the average level of the national economy. The average influence coefficient for this sector was 1.158, indicating that a 1-unit increase in final product demand for the digital core sector would lead to a corresponding increase of 1.158 units in the total output of the national economy. However, from a temporal perspective, the ranking of the digital core sector experienced fluctuations, suggesting an unstable level of influence and a relatively less significant radiation effect on other sectors of the national economy.

As for the digital foundational sector, based on Figure 2, it can be observed that its influence coefficients are relatively low, consistently falling below the average level of the national economy for all years except 2012. Over time, there has been a decreasing trend in the impact of the digital foundational sector on the national economy, with the influence coefficient declining from 1.029 in 2012 to 0.833 in 2020. This indicates that, as the overall national economy grows, the sector’s role in driving it forward becomes weaker compared to other sectors.

5.2.2. Sensitivity Analysis

From an overall perspective, during the period from 2012 to 2020, there were 16 sectors with responsiveness coefficients greater than 1. These sectors were predominantly found in fundamental industries such as energy and transportation. Notably, the sectors of chemical products and metal smelting and rolling processing products exhibited responsiveness coefficients exceeding 2.5, highlighting their substantial contribution to driving the national economy. However, it is important to note that, during periods of rapid economic development, these sectors can also become “bottleneck industries” that impose constraints on further economic growth (Figure 3).

Contrary to the influence coefficients, the responsiveness coefficients and rankings of the digital industry exhibit an upward trend. Specifically, the digital core sector demonstrates a noteworthy pattern. Its average responsiveness coefficient from 2012 to 2020 was 2.23, twice the average level of the national economy. Moreover, its ranking improved from 4th place in 2012 to 2nd place in 2020. This indicates that the digital core sector possesses a strong driving force for the economy. However, during periods of rapid economic growth, the digital core sector may encounter significant social demand pressure, potentially constraining overall economic development (Figure 3).

Regarding the digital foundational sector, although the responsiveness coefficients were below 1 from 2012 to 2018, both the ranking and responsiveness coefficients have displayed a clear upward trend. The responsiveness coefficient has increased by 133%, signaling a substantial rise in social demand for the digital foundational sector. This sector is progressively emerging as a pivotal industry that drives steady and healthy development of the national economy.

Whether it is the influence coefficient or the responsiveness coefficient, the digital core sector consistently surpasses the average level of the national economy. This indicates that the sector has a strong radiating effect and plays a supportive role, making it a crucial pillar industry for the development of the national economy. On the other hand, the digital foundational sector exhibits relatively low influence and responsiveness coefficients. This sector represents the industry derived from the digital transformation of traditional industries and may not have a significant short-term impact or driving force on the national economy. However, as the digital economy advances, the sector’s competitive advantage has notably strengthened.

In summary, the digital industry sectors are part of the backward linkages in the entire industry chain, primarily providing digital technology and products to other sectors. The analysis results show that there is an increasing demand for the digital industry in society, indicating that developing the digital industry is not a multiple-choice question but a mandatory course. By actively fostering the growth of the digital industry, it not only effectively promotes the digitalization upgrade of heavy industry sectors, energy sectors, and other industrial sectors, achieving “industrial digitization” and overcoming the development bottleneck of the manufacturing industry, but also drives the progress of the service industry and achieves structural reforms on the supply side.

6. Analysis of Complex Networks in the Digital Industry

In the previous section, the analysis focused on the relationship between the digital industry and other industry sectors using input–output perspectives, but it did not capture the structural characteristics of these sectors. Therefore, in this section, we construct a 42-sector industry linkage network based on the previously mentioned input–output table for the digital industry. By employing complex network analysis methods, we aim to explore the overall structural characteristics of China’s industry linkage network and analyze the evolving roles and positions of the digital industry within the network. This analysis provides valuable insights for optimizing and adjusting the industrial structure.

6.1. Network Construction

The total consumption coefficient establishes relationships from a demand perspective and explores the extent of association between downstream industries and their linkages. In this study, the network is constructed using the coefficient of total consumption as the foundational data. To further elucidate the primary network of industry associations, the study employs the Wioder combination index method to determine the threshold for association relationships [48]. The search is conducted column-wise on the matrix of total consumption coefficients, iterating through each column’s critical value. The selection of the Wioder combination index threshold is calculated based on the coefficient itself, providing a certain level of objectivity compared to other threshold selection methods. The specific calculation process is as follows:

$$w_{ij}={\sum }_{k=1}^n{[s(k,i)-100\times \frac{l(k,j)}{{\sum }_{k=1}^{n}l(k,j)}]}^{2}f\left(x\right)=\left\{\begin{array}{cc}\hfill \frac{100}{i}& k\le i\hfill \\ \hfill 0& k>i\hfill \end{array}\right.$$

where the Wioder index denotes the element in the i-$th$ row and j-$th$ column, where k represents the rank of the coefficient in descending order for each column. Here, i corresponds to the original rank before sorting and represents the k-$th$ coefficient in the j-$th$ column. By employing this method, the Wioder combination index is computed for all columns, resulting in a new matrix W. Threshold values for each column are derived from the W matrix, with values exceeding the threshold assigned as 1 and values below the threshold assigned as 0. Finally, the original order is restored, yielding the 42 × 42 adjacency matrix E. Concerning the matrix elements:

$$f\left(x\right)=\left\{\begin{array}{cc}\hfill 1& i\to j\hfill \\ \hfill 0& otherwise\hfill \end{array}\right.$$

Based on the aforementioned processing method, the industry linkage networks of China for the years 2012, 2016, and 2020 are depicted in Figure 4. Due to space constraints, this paper only displays the industry networks for these three years. To prevent self-loops in the constructed network, the input of an industry to itself is not taken into account in this study. In the figure, the size of each node corresponds to the number of industries connected to that particular node.

By examining Figure 4, we can see that the overall structure of China’s industry linkage network is relatively stable, with some local variations. The chemical products sector serves as the central node in the network, connecting to the largest number of industries. The digital core sector is positioned in the secondary core, while the digital foundational sector is located at the periphery of the network.

6.2. Analysis of Characteristics of Industry Interconnected Networks

6.2.1. Network Density

From

Table 8. Density of the industrial linkage network.

	2012	2013	2014	2015	2016	2017	2018	2019	2020
Network density	0.0488	0.048	0.045	0.050	0.048	0.0488	0.049	0.052	0.051

, it is evident that the maximum network density of China’s industry linkage network is merely 0.051, which indicates that the current stage of the network is in the developmental phase. The inter-industry relationships are not tightly connected at this stage.

6.2.2. Analysis of Scale-Free Network Characteristics

The degree distribution of the industry linkage networks in 2012 and 2020 is illustrated in Figure 5, demonstrating that the distribution conforms to a power-law pattern during the period from 2012 to 2020. This finding indicates that China’s industry linkage network exhibits significant characteristics of a scale-free network. The connectivity (degree) of each industry node displays an uneven distribution, with the majority of industries having fewer connections to other industries. Some examples include wood processing and furniture, waste and scrap, residential services, repair, and other services. Conversely, a small number of industries establish numerous connections and serve as core nodes in the network. Notable examples encompass chemical products, metal smelting, and rolling processed products within the manufacturing sector.

6.2.3. Small-World Analysis

Based on the data presented in

Table 9. Small-world index.

	2012	2013	2014	2015	2016	2017	2018	2019	2020
clustering coefficient	3.45	4.10	2.45	2.36	2.49	3.59	3.15	3.51	3.23
average path length	0.13	0.14	0.15	0.18	0.19	0.17	0.20	0.20	0.27

, it is evident that China’s industry linkage network demonstrates a higher clustering coefficient compared to a randomly generated network of similar scale. Moreover, it exhibits a smaller average path length, with a maximum of just four industries required to establish connections between any two industries. These findings suggest favorable liquidity and align with the characteristics of a small-world network. Considering the sensitivity of small-world networks, policy interventions targeting crucial nodes can swiftly disseminate throughout the entire national economic system.

6.3. Analysis of Individual Linkage Characteristics

6.3.1. Analysis of node degree

Table 10. Node degree.

	Digital Core Sector			Digital Foundational Sector
	Out Degree	In Degree	Total	Out Degree	In Degree	Total
2012	8	2	11	0	3	3
2013	10	1	11	0	2	2
2014	10	1	11	0	2	2
2015	10	1	11	0	2	2
2016	12	1	13	1	2	3
2017	10	2	12	1	1	2
2018	11	2	13	1	3	4
2019	11	2	13	3	3	6
2020	13	3	16	3	3	6

presents the node degrees of digital core sectors and digital foundational sectors from 2012 to 2020.

From the table, it is evident that the digital core sectors exhibit an outdegree equal to or greater than their indegree, and this outdegree gradually increases over time. In 2020, the node degree of the digital core sectors ranked second, highlighting their growing significance. The digital foundational sectors have also transitioned from peripheral positions within the network to more central ones. In recent years, the country has made substantial efforts to develop the digital economy, resulting in a significant surge in the demand for digital industries across diverse sectors. As crucial producers of digital technologies, the digital core sectors have become major consumers for an expanding range of industries, providing vital support to other sectors. The digitization of industries has further led to the digital foundational sectors serving as suppliers to an increasing number of sectors, demonstrating a sustained growth trend in external provision. Additionally, it is noteworthy that the second industry holds a prominent position in the node degree ranking, indicating that the manufacturing industry continues to be the dominant sector in China, exerting strong influence.

6.3.2. Analysis of Eigenvector Centrality

In general, China’s chemical products, metal smelting and rolling processed products, digital core sectors, wholesale and retail, leasing and business services, and real estate consistently rank high in terms of eigenvector centrality. This indicates that these industries occupy key bridge positions within the industry network and play a vital role in its structure. Upon analyzing Figure 6, it is evident that the digital core sectors have experienced significant growth in eigenvector centrality, increasing from 0.315 in 2012 to 0.429 in 2020, representing a growth rate of 36.3%. Moreover, their ranking has shifted from the third position in 2012 to the first position in 2020. This demonstrates the pivotal role of the digital core sectors in ensuring the flow of the industry network. They not only export products to numerous downstream industries but also connect with critical sectors within the industry system. The development of these sectors can greatly influence the stability of the industry system, indicating the emerging dominance of the digital industry in the overall economy.

Although the digital foundational sectors do not rank as high as the digital core sectors, their eigenvector centrality has experienced a remarkable increase of 80.7%. This signifies that the digital foundational sectors are gaining more influence and hold growing significance in the entire industry network, highlighting their enhanced value.

By combining the node degree indicator, we have identified a shift in influence between the secondary and tertiary industries. Among the top ten industries in terms of eigenvector centrality ranking, the proportion of the tertiary industry has increased from 30% in 2012 to 60% in 2020. This trend signifies a gradual decline in the value of the manufacturing industry and a progressive rise in the influence of the service industry. It is anticipated that, in the future, the service industry will further encroach upon the manufacturing sector and emerge as a vital driver of economic development.

Overall, although the digital core sector has not yet occupied a central position, it has become an indispensable sector within the industrial system. Furthermore, based on the network indicators, we can see that the digital industry sectors serve as significant suppliers and are connected to the pivotal sectors within the industrial network. Moreover, considering the small-world characteristics of China’s industry linkage network, expanding the development of the digital economy and its industries can efficiently radiate throughout the entire industrial system, as well as promote the optimization and upgrading of the industrial structure.

7. Conclusions

This article presents a comprehensive analysis by constructing a national input–output table and establishing a sequence for the digital industry in China from 2012 to 2020. It utilizes input–output analysis and complex network analysis to explore the interdependent effects and influences between the digital industry and other sectors, Moreover, it examines the structural characteristics and development trends of the digital industry within the industry network. The key findings are as follows:

(1) The digital core sectors primarily rely on the secondary industry as a foundation, utilizing its resources for growth. They also provide support to the tertiary industry, facilitating its transformation and advancement.

(2) The digital industry sectors play a vital role in the backward linkage of the industry chain, acting as intermediate demand industries that drive the transformation and development of other sectors.

(3) China’s industry linkage network demonstrates characteristics of low density, scale-free distribution, and small-world properties. The connectivity between industry nodes is uneven.

(4) The manufacturing industry remains dominant in China, and the tertiary industry is gradually encroaching upon it and becoming a significant sector for economic development.

(5) The digital foundational sectors are at the periphery of the network and have not developed a core advantage. The digital core sectors have not yet become the leading industries, but they have emerged as pivotal departments within the industry system, indicating the growing dominance of the digital industry in the overall economy.