Analysis of the evolutionary characteristics of indirect energy ow and dependence among Chinese industrial sectors


 Background: The diversification of product production and consumption generates closer links between industrial sectors and increases the complexity of indirect energy flows between industrial sectors and interdepartmental interdependence. Methods: We calculated the indirect energy flows between various industrial sectors in 2002, 2007, 2012 and 2017. Then, we have built four indirect energy flow networks and explored the characteristics and the interdependence of indirect energy consumption between sectors. Finally, a quadratic assignment procedure correlation analysis was performed to clarify the relationship between the indirect energy flow relationship and the dependence relationship between industrial sectors.Results: Different industrial sectors play different roles in the process of indirect energy consumption, with a more concentrated indirect energy supply among industrial sectors compared with consumption and a gradual shift in the indirect energy supply from the chemical industry to the service industry. Higher and more stable flow paths that carry indirect energy flows and clearer interdepartmental dependencies are reflected in the upstream and downstream links of the industrial chain. The correlation between indirect energy flows and interdepartmental dependencies is gradually increasing but requires improvements to further optimize China’s industrial structure and reduce energy consumption.Conclusions: Efforts should be made to reduce the energy supply in the chemical sector, optimize the quality of the energy supply in the service sector, and reduce energy consumption. Appropriate attention should be focused on the indirect energy flow relationship between the upstream and downstream industries of the industrial chain, and the integrity of the domestic industrial chain can be improved to reduce the total energy consumption.

Background 31 It has been six years since China's "dual control" action on total energy 32 consumption and intensity was proposed on October 26, 2015. This action controls the 33 total amount and intensity of energy consumption at the regional level, but the current 34 control of total energy consumption is still severe in some regions. Energy is one of the 35 foremost elements of human economic activities, and it is consumed directly or 36 indirectly by the main body of economic activities [1,2]. Direct energy consumption 37 methods include the consumption of products, such as oil, coal, natural gas, and 38 minerals. The indirect method refers to the indirect consumption of resources through 39 the consumption of economically produced final products or intermediate products [3]. 40 necessary to distinguish between the direct energy consumption of a product or industry 48 and the indirect energy consumption, which includes intermediate production and 49 consumption. At the same time, it is also necessary to analyze energy consumption, that 50 is, the energy flow between sectors. Embodied energy consumption not only considers 51 direct energy consumption but also considers indirect energy consumption, which has 52 been less studied in previous research. Therefore, scholars have conducted relevant 53 research on calculating and identifying the influencing factors of embodied energy and 54 the flow of embodied energy in the trade process [6,7]. 55 Although research on direct energy consumption and embodied energy 56 consumption has gradually matured, only a few scholars have analyzed indirect energy 57 consumption. In reality, however, almost the production and service provision of almost 58 any commodity will indirectly consume energy; therefore, indirect energy consumption 59 has a huge impact on total energy consumption and emission control. Therefore, it is 60 necessary to analyze indirect energy consumption separately as a research object to 61 more effectively improve current energy consumption and reduce total energy 62 consumption. Previously, scholars mainly conducted research on the influencing 63 factors and consumption structure of residents' indirect energy consumption [8][9][10]. 64 Because energy is consumed in all aspects of social production and life, some scholars 65 have also conducted research on indirect energy consumption from the perspective of 66 various industrial sectors. Harun M quantified the total, direct and indirect energy 67 intensity of the industrial sector in Malaysia and identified the sectors that led to 68 increased energy consumption [11]. Yuan Y analyzed the indirect energy consumption 69 of China's tourism industry [12]. Wang B analyzed the energy flow network between 70 Chinese industrial sectors and found that general equipment manufacturing and 71 electrical equipment manufacturing are the key sectors of indirect energy 72 consumption [13]. However, the situation of indirect energy flow between industrial 73 sectors is complicated, and limited research has focused on the indirect energy flow 74 between industrial sectors and the dependence control relationship between industrial 75 sectors; therefore, a relevant analysis has been performed on this issue. 76 First, we need to measure indirect energy consumption. The existing energy 77 consumption measurement methods are mainly divided into measurement methods 78 based on the consumption life cycle and measurement methods based on an input-79 output table. The measurement method based on the consumption life cycle is mainly 80 used to measure the indirect energy consumption of residents. Moreover, the calculation 81 method needs to clarify the data throughout the whole life cycle of a product from raw 82 material acquisition to final consumption, although the operability is relatively low. 83 Input-output analysis is an economic quantitative analysis method proposed by Leotief. 84  Yearbook. Due to the inconsistency between the industrial sector classification in the 135 "China Input-Output Table" and the industrial sector classification in the "China 136 Energy Statistical Yearbook". To ensure the accuracy of the calculation, Jiang's method 137 was used and the number of industry sectors was merged into 30 to ensure consistency 138 with the energy consumption table by industry in the "China Input-Output Table" and 139 " China Energy Statistical Yearbook"[20]. The merged industry sector classification is 140 shown in Table 1  149 where x ij represents the number of products or services of sector i directly consumed 150 in the production process of the product and operation of sector j; x j is the total input 151 of sector j; and a ij is the quantity of products or services of sector i directly consumed 152 by the unit's total output of sector j in the production and operation process. The matrix 153 A formed by a ij is the direct consumption coefficient matrix. 154 The complete consumption coefficient matrix can be calculated on the basis of the 155 direct consumption coefficient matrix, as shown in Formula (2)

212
where i, j, k represents the industry sector, g jk represents the number of shortcuts 213 between j and k, g jk (i) represents the number of shortest paths between sectors, and 214 B i represents the betweenness centrality of point i, and the value range is [0,1]. 215 (3)Average shortest path length. The speed and efficiency of indirect energy 216 flow between any two sectors can be measured by the average shortest path length L of 217 the complex network, that is, the number of edges over which indirect energy flows 218 from sector i to sector j. 219 where N represents the number of nodes in the network, that is, the number of sectors, 221 and d ij represents the number of edges on the shortest path between sector i and sector 222 j, that is, the distance between the two sectors. 223 (4)Average clustering coefficient. The average clustering coefficient of the 224 network is the average of the clustering coefficients of all industrial sectors, reflecting 225 the tightness of the network. The clustering coefficient of a node refers to the possibility 226 that all nodes connected to the node in the network are also connected. The calculation 227 formula for the clustering coefficient of node i is shown in Equation (8). 228 where C is the average clustering coefficient of the IEFN and C i = , which is 230 the average clustering coefficient of sector i. In a directed network, when node i has 231 k i nodes directly connected to it, k i (k i − 1) represents the maximum number of 232 edges that may exist between these k i nodes and M i represents the number of edges 233 that actually exist. 234 (5)Modularity. Community detection can make the nodes in the network form 235 clusters in a specific way and divide them into different communities. The industry 236 sectors within the community are closely connected, and the connections between 237 communities are relatively loose. We use the modularity maximization method 238 proposed by Blondel et al. for community detection[21], and the modularity calculation 239 is shown in Equation (9). 240 where Q represents modularity, m is the weight of the edge in the network, A ij is 242 the weight of the edge between node i and node j, k i and k j are the sum of the weights 243 of all edges connected by two nodes, and is the expected value of A ij under 244 random conditions. 245 and z i and y i represent the input and output generated between sector i and the 252 external environment, respectively. 253

Measurement of dependency
The total input or total output of inflow and outflow sector i are shown in 254 Equations (5) and (6), respectively. 255 When the system is in a stable state, the total amount of indirect energy flowing 258 into industrial sector i is equal to the outflow, namely: 259 The control analysis based on the concept of an "ecological network" originated 262 from Patten and was further developed by researchers such as Schramski[22]. Control 263 analysis can identify the control effect of the indirect energy flow of a certain sector on 264 other sectors. In other words, it can identify the degree of dependence of one sector on 265 another sector. We introduce the dependency matrix CN = (cn ij ) among sectors to 266 express the degree of dependence and the degree of control between the industrial 267 sectors. 268 where g ij and g ij ′ represent the interdepartmental flow of total output and total input, 273 respectively; N and N ′ represent the dimensionless cumulative output and input flow 274 matrices, respectively; and cn ij indicates that sector i controls sector j. Thus, the 275 dependence of sector j on sector i is . 276 QAP related analysis 277 The quadratic assignment procedure (QAP) is a correlation analysis that obtains 278 matrix correlation coefficients by comparing random replacement matrices and 279 performs nonparametric correlation tests, which can be used to study whether two 280 "relationship" matrices are related. The specific calculation steps are as follows: First, 281 all the values of each matrix are regarded as a long vector, and the correlation 282 coefficient R between the two vectors can be calculated, as shown in Equation (12) where the R value is the observed correlation coefficient. Second, we perform random 285 replacement of one matrix datum, calculate the correlation coefficient between the 286 replaced matrix and the other matrix, and repeat the calculation to obtain a correlation 287 coefficient distribution. Finally, the observed correlation coefficient was compared 288 with the distribution of the correlation coefficient calculated according to the 289 rearrangement to determine its significance level [23]. Because the amount of energy 290 flow between industrial sectors, that is, the degree of dependence, is "relational data", 291 the QAP is used for the correlation analysis. 292

Results and discussion
293 Small world features 294 A small-world network refers to a network in which most nodes are not adjacent 295 but can reach each other through a small number of nodes. This type of network can be 296 measured by two indicators, the average clustering coefficient and the average shortest 297 path length. As shown in Table 2, we find that IEFN-1 has a large clustering coefficient 298 of 0.651, indicating that the network has a high effective correlation degree, and most 299 industrial sectors have a high degree of clustering. IEFN-1 has a shorter average 300 shortest path length of 1.113, and energy flows faster. Combining the values of these 301 two indicators, it can be seen that IEFN-1 is a small-world network. According to the 302 data in Table 2, these four indirect energy flow networks all have small-world 303 characteristics, which means that the indirect energy flow relationship between various 304 industrial sectors in the network is relatively close and the impact on one sector may 305 quickly spread to other sectors in the network, thus leading to changes in the entire 306 industrial system. 307

Identification of key industry sectors
309 Key industrial sectors can be identified based on two aspects: point intensity and 310 the "media" role. Point intensity is used to measure the influence intensity of the 311 industrial sector. The greater the point intensity, the more important the industrial sector. 312 Intermediary centrality is used to measure the "media" role of the industrial sector. The 313 greater the intermediary centrality, the more important the industrial sector. In IEFN, 314 sectors with greater strength or intermediary centrality are key industrial sectors. 315  Table 3 shows the top ten sectors of the intermediary centrality of each 355 network. Six industrial sectors are always in the top ten sectors, which have not changed 356 much; however, the intermediary strength of each sector changes dynamically. 357

The influence intensity of the industry sector
Relatively speaking, the PPC and the MSRP are sectors with important intermediary 358 roles. 359 between various sectors is shown in Figure 5. The IEFN-1, IEFN-2 and IEFN-3 results 366 are relatively similar. They are divided into community I, in which the CMI is the 367 indirect energy supply center, and community II, in which the MSRP as the indirect 368 energy supply center. The number of sectors included in community Ⅰ is much larger 369 than that in community Ⅱ. The indirect energy outflow of community II is always 370 greater than the inflow, which has a strong indirect energy spillover effect. A 371 comparison of IEFN-1 and IEFN-2 shows that the PPCESGM, the EMEM, and the GPS 372 have changed from community Ⅰ to community Ⅱ. The MPI and the GEM have changed 373 from community II to community I. A comparison of IEFN-2 and IEFN-3 shows that 374 the GPS has transformed from community II to community I and the instrument, meter 375 and cultural office machinery manufacturing industry has transformed from community 376 I to community II. 377 The organizational structure of IEFN-4 has changed significantly, and some 378 industrial sectors have been divided into communities with the OSI as the core. 379 Compared with IEFN-3, the PPCESGM and the CSI in IEFN-3 community II are 380 divided into the new community III in IEFN-4. The AFAHF, the OGE, the FMTP, the 381 TXI, the NMOMD, the CEOEEM, the WRAC and the OSI in community I are covered 382 and divided into new community III. Community III takes the OSI as the core of the 383 association, including all aspects of social life. This finding shows that the service 384 industry has been involved in all aspects of social life and has become the main source 385 of indirect energy consumption. 386 387 1 connected to the edges will be controlled and then spread to the entire industrial system, 401 thereby reducing the overall energy consumption. 402 The top 1.31%, 1.22%, 1.15%, and 1.16% of the edges in each network carry 403 9.36%, 15.91%, 14.55% and 11.08% of the indirect energy flow, respectively. We use 404 these edges as the starting edges to identify the path of indirect energy flow. The input 405 sector of the starting edge is the starting node, and the target node in the starting edge 406 is used as the second input sector to continue to capture the industry sector that has the 407 largest edge-weight relationship with the second input sector. This process is repeated 408 until the last sector returns to the penultimate sector to identify the critical path of each 409 year, as shown in Table 5 Figure 7 shows the dependency ratio between industry sectors (from column to 423 row). The average dependency among network sectors is 0. 324, 0.341, 0.326, and 0.386. 424 The closer the value of dependence between sectors is to 1, the stronger the dependence. 425 Overall, the interdepartmental dependency control relationship in IEFN-4 is obvious. between industrial departments, we performed a QAP correlation analysis to test the 457 correlation between the dependence matrix and the indirect energy flow matrix. As 458 shown in Table 6, a negative correlation was observed between inter-sectoral 459 has become stronger, which shows that the adjustment of China's industrial structure 469 has achieved remarkable results and the industrial chain of commodity production and 470 service has been gradually improved. However, the similarity between the two is not 471 high, and the industrial structure still needs to be further optimized. To reduce the total 472 energy consumption, necessary attention should be focused on the indirect energy flow 473 relationship between the upstream and downstream industries of the industrial chain, 474 and the integrity of the domestic industrial chain should be improved. 475

477
The first column is the Pearson correlation coefficient between the two relationship matrices.

478
industrial sectors in the network is relatively close and an impact on one sector may 501 quickly spread to other sectors in the network. The evolution of individual 502 characteristics of the network shows that different industrial sectors play different roles 503 in the process of indirect energy consumption. The CMI and the MSRP are the main 504 indirect energy suppliers; the PPC and the MSRP play an intermediary role; and the 505 MPI and the EMEM are the main indirect energy consumers. Therefore, when 506 formulating related policies to reduce industrial energy, it is necessary to formulate 507 corresponding strategies for industries that assume different roles. For example, in the 508 process of curbing the flow of inefficient indirect energy, the path of consumption can 509 be blocked by controlling industrial sectors that have a mediating role. Moreover, the 510 consumption of ineffective or inefficient indirect energy can be reduced to reduce 511 energy consumption. 512 (3)In the process of reducing energy consumption, it is necessary not only to 513 pay attention to the key sectors that assume various roles but also the critical path of 514 indirect energy consumption. The critical path identification results show that the flow 515 paths that carry a high and relatively stable flow of indirect energy are all flow paths 516 based on the production situation of the industrial chain. Therefore, it is necessary to 517 reduce energy consumption from the perspective of the industrial chain. For example, 518 for the MSRP → the MPI, which has always carried the most indirect energy flow, it is 519 necessary to focus on the energy consumption of this path. The supply of ineffective 520 energy in the MSRP must be reduced, the energy consumption quality of the MPI must 521 be improved, and a relative balance between energy supply and consumption must be 522 formed. Energy supply is driven with energy demand, thereby reducing energy 523 consumption. 524 (4) A dependency correlation analysis results show that the more explicit 525 dependence between industrial sectors is reflected in the upstream and downstream 526 links of the industrial chain. Therefore, reducing energy consumption needs to proceed 527 starting from the overall situation of the industrial sector. Based on the upstream and 528 downstream relationships between industrial departments, cross-departmental 529 coordination policies should be formulated to promote the coordination of industrial 530 departments to reduce energy consumption. The correlation between dependence and 531 indirect energy flow is increasing as a whole, and the similarities between the two are 532 becoming stronger. This finding shows that the adjustment of China's industrial 533 structure has achieved remarkable results, and the industrial chain of commodity 534 production and service has been gradually improved. However, the similarity between 535 the two is not high, which indicates that the industrial structure still needs to be further 536 optimized. Appropriate attention should be focused on the indirect energy flow 537 relationship between the upstream and downstream industries of the industrial chain, 538 and the integrity of the domestic industrial chain can be improved to reduce the total 539 energy consumption. 540