Indirect energy flow between industrial sectors in China: A complex network approach

Energy 94 (2016) 195e205

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Energy journal homepage: www.elsevier.com/locate/energy

Indirect energy flow between industrial sectors in China: A complex network approach Xiaoqi Sun a, b, c, Haizhong An a, b, c, *, Xiangyun Gao a, b, c, Xiaoliang Jia a, b, c, Xiaojia Liu a, b, c a b c

School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China Key Laboratory of Carrying Capacity Assessment for Resource and Environment, Ministry of Land and Resources, Beijing 100083, China Lab of Resources and Environmental Management, China University of Geosciences, Beijing 100083, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 November 2014 Received in revised form 12 September 2015 Accepted 19 October 2015 Available online 21 November 2015

Indirect energy consumption accounts for a large proportion of the all energy used in processes to make the final products and thus exerts huge pressure on environment. Structural analysis of indirect energy flow network is a prerequisite for solutions to energy related problems. The aim of this study is to reveal the structure of indirect energy flow network and its change from 1993 to 2007. To this end, we constructed three directed weighted IEFNs (indirect energy flow networks) with 28 sectors on the basis of three basic inputeoutput tables from 1997, 2002, and 2007. By analyzing the clustering coefficient and the average path length of the networks, we obtained the small world nature of IEFNs. In the same study, we identified key sectors of the IEFNs on the basis of three centrality indicators from complex network theory, namely degree centrality, eigenvector centrality, and betweenness centrality. In addition, we analyzed the indirect energy flow paths in the network. Based on the knowledge of the structure of IEFNs and its trend, we discussed the possible policy implications. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Inputeoutput table Complex network Indirect energy flow China

1. Introduction It is a common practice to assess energy consumption in terms of direct energy. However, producing goods and services consumes not only direct energy such as oil, gas, coal etc. but also indirect energy. Indirect energy or embodied energy is the energy consumption embodied in the goods and services to make the final products [1,2]. Using data from 2007, it has been reported that in the Chinese economy indirect energy consumption accounts for 80.6% of all energy used in processes to make the final products [3]. As an export and investment driven economy, China has become the largest indirect energy exporter in the world and is to replace the United States as the world's leading indirect energy consumer in 2027 [4]. As a consequence, China has been the world's top emitter of greenhouse gases [5] and suffered serious haze pollution [6]. With this magnitude of potential indirect energy consumption and air pollutions, it is important to study indirect energy consumption in China.

* Corresponding author. School of Humanities and Economic Management, China University of Geosciences, Beijing 100083, China. Tel.: þ86 10 82323783. E-mail address: [email protected] (H. An). http://dx.doi.org/10.1016/j.energy.2015.10.102 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

Previous indirect energy research focused on indirect energy flows in international trade by calculating energy embodied in exported and imported commodities and services with IeO (InputeOutput) tables [4,7e14]. These studies presented similar conclusions, that China is an energy exporter to foreign countries, and the details of these findings, not readily foreseen, further presents the importance of indirect energy research. Different from previous studies, this study aims to reveal the structure of indirect energy flow networks and its change over the time surveyed, which is a systemic analysis at the sector level. There are two theoretical reasons behind this. Firstly, it is sectors that produce goods and services for intermediate uses and final uses. Secondly, the structure is closely related to its systemic functions [15e18]. Thus, knowing the structure of indirect energy flow network offers the prerequisite for coping with energy related problems and thus for achieving a sustainable Chinese economic system. For our purpose, the structural analysis is the task of identifying critical sectors and vital interdependencies between sectors and analyzing their impacts on the efficient and continuous energy consumption. Though broad relationships between main sectors can be obvious, in the complex network of an economy, some vital interdependencies and features of nodes are counterintuitive.

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The input and output of commodities and services between sectors imply indirect energy flow between them. National inputeoutput tables map well the flows of goods and services between the sectors of an economy [19]. Thus, it is well suited in studying the flows of indirect energy. Additionally, sectors of different sizes interact with each other by supplying and consuming indirect energy and form a complex process [20]. These interactions on a systemic level can be understood by complex network analysis [21]. Complex network theory is a useful analytical framework to investigate the properties of nodes, of the structure, and of interactions between two nodes [15,22e24]. The usefulness of this approach has been proved by many energy studies [25e35]. The core idea of complex network analysis is to abstract the interactions between various nodes of a real, complicated world as a complex network. In this study, each sector corresponds to a node, and the flow of indirect energy from one sector to another is set as an edge. Then a directed and weighted complex network is built, namely the IEFN (indirect energy flow network). In complex network theory, identifying the sectors' roles in the IEFN is to measure node centrality appropriately [20]. The rest of this paper is as follows: Section 2 introduces the data and methodologies used in this study. Section 3 presents results of centralities in terms of different measures, key interdependencies in IEFNs, and the trends of IEFNs. This section also includes some related analyses. Section 4 provides discussions and policy implications followed, finally, by our conclusion.

Fig. 1. The principle of inputeoutput balance of embodied energy.

di þ

n X

0 εj  xji ¼ εi  @

j¼1

n X

xij þ fi Aði ¼ 1; 2; :::; n; j ¼ 1; 2; :::nÞ

j¼1

(1) where di denotes direct energy input of sector i; εj denotes the indirect energy intensity of sector j; xji denotes the intermediate input j to produce product i; and fi denotes the sum of final conP sumption. εi  nj¼1 xij stands for the indirect energy output. Thus, the entire table can be expressed in the following matrix equation:

2. Data and methods

DT þ X T Z T ¼ YZ T

2.1. Data

1 d1 B d2 C B C B: C T C where DT ¼ B B : C; X B C @: A dn 0 n P x1j þ f1 0 : B B j¼1 B B 0 : B Y¼B : : B B : B @ 0 : :

(2)

0

The basic IeO table is issued every 5 years in China, and the latest one (the 2012 edition) has not been issued yet. Therefore, the basic IeO tables used in this study are the 1997 edition, the 2002 edition, and the 2007 edition. The basic IeO tables and original energy data used in this study are derived from the China Statistical Yearbook from 1993 to 2010 and the China Energy Statistical Yearbook from 1993 to 2010 (http://www.stats.gov.cn/english/ Statisticaldata/AnnualData/). Because the sector classifications of basic IeO tables are changing and sector classifications of basic IeO tables are not identical with those of energy balance sheets, we combine them into a 28-sector table for the convenience of data processing without excluding important information (see Table A.1 in Appendix A). In this paper, we choose the total direct energy consumption by every industrial sector data to calculate indirect energy consumption. Thus, all kinds of primary energy sources have been taken into consideration. In addition, we adopt 10,000 tons of standard coal equivalent (tce) as a common basis of energy consumption. Because the basic IeO table is issued every 5 years, we use the average direct energy consumption from the corresponding period for a more comprehensive reflection of reality, rather than using the energy consumption for the final year of that period. After data consolidation, we process the indirect energy data based on the method proposed by Ref. [12] as follows: Fig. 1 shows the principle of inputeoutput balance for Producer i in terms of indirect energy flow. One point of applying this principle is worthy of note. When working in physical energy units, in accordance with the law of conservation of energy, additional energy inputs, di , to the system from the earth must be accounted for, see Eq. (1). This is entirely different from the simple extension of P monetary inputeoutput balance, εi Xij ¼ εi Xi , which has been

1

0

x11 B : B ¼B B : @ : x1n :

: :

: :

:

:

:

:

: : : 1

0 1 1 ε1 xn1 B ε2 C : C B C C T B : C : C C; and C; Z ¼ B B : C : A @ A : xnn εn

0

C C C C : C C : C C : C n P xnj þ fn A j¼1

To calculate the value of Z, Eq. (2) needs to be transformed into Eq. (3) (Y T ¼ Y, as Y is symmetric matrix):

D þ ZX ¼ ZY

(3)

Thus, Z denotes the indirect energy intensity vector, which can be calculated because ðY  XÞ is reversible and guaranteed due to the construction standard of economic inputeoutput table [37]:

Z ¼ D  ðY  XÞ1

(4)

The indirect energy coefficient is a critical part of this method, and it is a good measurement of the indirect energy efficiency that we will use in Section 3. 2.2. Complex network technique A complex network consists of nodes and edges that link the nodes, as shown in Eq. (5):

G ¼ ðN; EÞ

(5)

i¼1

criticized for not considering energy conversation conditions [36,37]. For sector i, the balance of indirect energy is as follows:

where G represents a complex network; N denotes the set of nodes in the network; and E represents the set of edges in the network.

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If i is a network node, we define i2N. If there is a link between i and j, the direction of the link is from i to j, ði; jÞ2E. In addition to the direction of indirect energy flow in the network, the edges are also weighted. If ði; jÞ2E we write ei;j > 0; otherwise, we write ei;j ¼ 0. The matrix of the indirect energy flow between industrial sectors can thus be expressed in Eq. (6):

2

3 e11 : : : e1n 6 : : : 7 6 7 E¼6 : 7 : 6 : 7ði; j ¼ 1; 2; :::; nÞ; where eij ¼ εi  xij 4 : : : 5 en1 : : : enn

(6)

For this study, the other two useful concepts from complex network theory are in-degree and out-degree. The in-degree of i is the number of starting nodes that go to node i; the out-degree of j is the number of destination nodes that node j can reach. On the basis of these notations and equations, the directed, weighted IEFN can then be established. In addition, we established three IEFNs here, as our analysis involves three inputeoutput tables. Fig. 2 shows the IEFNs in this study. From left to right, Fig. 2(a)e(c) represents IEFN from 1993 to 1997, 1998 to 2002, and 2003 to 2007, respectively. For the purpose of this paper, we will analyze the small world nature of the IEFNs first, followed by analysis of different roles of each sector playing in the IEFNs from degree centrality, eigenvector centrality, and betweenness centrality. In addition, we will identify the key indirect energy flow paths in IEFNs. All the empirical results are derived from the complex network models and reported as calculated in the models to two decimal places. 3. Results' analyses First of all, we define the three networks in this study as follows: IEFN from 1993 to 1997 is defined as IEFN-1, IEFN from 1998 to 2002 as IEFN-2, and IEFN from 2003 to 2007 as IEFN-3. All these networks have 28 sectors, while there are 750 edges in IEFN-1, 749 edges in IEFN-2, and 761 edges in IEFN-3. For readability and simplicity of result presentations and discussions, we also define every sector's abbreviations (see Table A.2). 3.1. The small world nature of IEFNs Small world network refers to the network in which most nodes are not neighbors of one another, but where most nodes can be reached from every other by a small number of steps [18]. Expressing this intuitive notion in network parlance, this type of network is detected by two indicators: (1) the clustering coefficient, defined as the ratio N/M averaged over all nodes, where N is the number of edges between the neighbors of node i, and M is the

197

maximum number of edges that could exist between the neighbors of node i; and (2) the average path length, defined as the number of edges in the shortest path between two nodes, averaged over all pairs of nodes [15]. Applying these indicators to the indirect energy flow data, we obtained IEFN-1 with a high clustering coefficient of 0.955 and a short average path length of 1.045, IEFN-2 with a high clustering coefficient of 0.954 and a short average path length of 1.046, and IEFN-3 with a high clustering coefficient of 0.97 and a short average path length of 1.03. Taking IEFN-1 as an example, the high clustering coefficient means most sectors are highly clustered, yet each sector can reach another sector in 1.045 steps. These three networks of indirect energy flow are thus confirmed with small world nature. The small world nature has implications for the dynamics of processes taking place on networks [18]. Changes in key sectors will affect significantly the systemic functions. In the context of indirect energy flow, for example, this property implies that a supply disturbance in key sectors will spread very quickly to most sectors and thus leading to turmoil of the overall economy. It is very sensitive and fragile under certain circumstance. On the other hand, it implies clean productions in key sectors will significantly improve the cleanness level of the whole economy.

3.2. Key sectors in IEFNs based on degree centrality Disturbance to different sectors will have various impacts. Therefore, it is necessary to identify key sectors that are likely to affect aggregate economy or systemic functions significantly. There are several ways to measure one sector as a key sector. The first one is weighted degree of one sector, defined as the sum of weights of sectors with which it is connected. The bigger the weighted degree of one sector is, the more important it is. Corresponding sectors' inputs and outputs there are weighted in-degree and weighted outdegree. In complex network theory, this is called degree centrality. We write the weighted in-degree of node i, Ii , as the sum of the amount of indirect energy from sector j to sector i, as shown in Eq. (7):

Ii ¼

X eji

(7)

j¼1

where eji denotes the amount of indirect energy from sector j to sector i. The larger one sector's weighted in-degree is, the more indirect energy consumption there is. As shown in Fig. 3, we can see that 1/5 of the sectors consumed around half of the indirect energy in IEFN-1, IEFN-2, and IEFN-3 and there is no significant change on pattern occurred during these three periods. Additionally, the proportion of indirect energy

Fig. 2. (a) IEFN (1993-1997), (b) IEFN (1998-2002), (c) IEFN (2003-2007). Note: The node's size denotes the weighted in-degree; the larger the node is, the larger the weighted indegree is. The color's depth denotes the weighted out-degree; the deeper the color is, the larger the weighted out-degree is. The line's thickness denotes the energy flow's weight; the thicker the line is, the greater the energy flow is. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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[38,39]. It is well known that China is the manufactory of world. In addition, because of the rapid development of infrastructure and housing market, huge indirect energy flows to construction sector. Though the relative importance of services is unstable, with the trending transformation from industry to services, we can project with some confidence that it will become one of top three indirect energy consumers among all sectors. Similarly, we used the weighted out-degree Oi , which is the sum of the amount of indirect energy flow from sector i to sector j, as expressed in Eq. (8):

Oi ¼

X

eij

(8)

j¼1

Fig. 3. Cumulative distributions of weighted in-degree. Note: On the horizontal axis, we process sectors using the following procedures: (1) ranking sectors in descending order according to their weighted in-degree; (2) using the ranks to calculate cumuP lative ranks, i.e., n=28, n ¼ 1, 2, 3, …,28. This process procedure similarly applies to Figs. 7 and 10. 1

consumption of the first 21.43% of sectors in IEFN-2 is higher than that in IEFN-1 by 2.94% and that in IEFN-3 by 0.99%. However, if delving into details of the indirect energy consumption over these three periods, we find significant positions change of sectors. The changes in the specific sectors are shown in Table 1. In terms of indirect energy consumption, construction, chemical industry, services, metals' smelting, agriculture, machinery, and non-metallic products are the central sectors consuming over 55% of indirect energy in IEFN-1; construction, services, chemical industry, metals' smelting, machinery, agriculture, and other electronic equipment are the central sectors consuming over 57% of the indirect energy in IEFN-2; and in IEFN-3, the central sectors consuming over 51% of the indirect energy are metals' smelting, construction, chemical industry, services, machinery, other electronic equipment, and electrical equipment. The structures of these IEFNs are significantly different from that of direct energy consumption (see Fig. 4(a)e(f)). Among these central sectors, the relative importance of metals' smelting increases significantly and that of agriculture declines. The reason behind this change relates to the in-degree of sectors (Table B.1 in Appendix B), the embodied energy coefficient (see Fig. 5), and the monetary intermediate input (see Fig. 6). For instance, construction sector's in-degree is lower than that of the chemical industry sector and its embodied energy coefficient is smaller than that of chemical industry. However, the construction sector ranks above the chemical industry, and thus the intermediate part is the determinant force. In other words, construction has input linkages to those with higher indirect energy supply than chemical industry does. The change under discussion is also related to the economic structure adjustment in China. Over the past 30 years, the driver of China's economic growth has transformed from agriculture to industry

where eij denotes the amount of indirect energy flow from sector i to sector j. The greater one sector's weighted out-degree is, the more indirect energy it supplies. Fig. 7 reflects the total indirect output situation during these three periods. During these three periods, 1/5 of sectors supply more than half of the indirect energy. The distribution of sectors supplying indirect energy is more concentrated from 2003 to 2007 than during the other two periods. Table 2 shows the changes in indirect energy output in detail. Chemical industry, metals' smelting, non-metallic products, electric and heat power production, agriculture, metal products, and fuel processing are the seven central sectors “supplying” over 58% of the indirect energy flow to other sectors in IEFN-1. In IEFN-2, these central sectors are metals' smelting, chemical industry, transport, non-metallic products, fuel processing, electric and heat power production, and services supplying over 58% of the indirect energy to other sectors. In IEFN-3, metals' smelting, chemical industry, electric and heat power production, non-metallic products, fuel processing, transport, and machinery are the central sectors supplying over 60% of the indirect energy flow to other sectors. It is observed that the central sectors become more and more important in supplying indirect energy. The changes in sector rankings in terms of indirect energy output can be explained by the monetary intermediate output, the embodied coefficient, and the out-degree. Take the metals' smelting sector and the chemical industry sector as an example. The outdegrees of both sectors are 28 (see Table B.1 in Appendix B). In IEFN-1, the weighted out-degree of the chemical industry sector outweighs that of the metals' smelting sector, which is attributed to the fact that the chemical industry sector's intermediate monetary output is higher than metals' smelting sector's output by 69.27%, even though the metals' smelting sector's embodied coefficient is larger than that of the chemical industry sector by 54.55% (see Figs. 5 and 8). 3.3. Key sectors in IEFNs based on eigenvector centrality A sector with huge consumption or supply volume is definitely a key sector. However, a sector can also be considered as a relatively

Table 1 Results of weighted in-degree. Period

1993e1997

1998e2002

2003e2007

The first 10% of sectors

1. Construction 2. Chemical Industry 3. Services (plus the first 10%) 4. Metals' Smelting 5. Agriculture 6. Machinery 7. Non-metallic Products

1. Construction 2. Services 3. Chemical Industry (plus the first 10%) 4. Metals' Smelting 5. Machinery 6. Agriculture 7. Other Electronic Equipment

1. Metals' Smelting 2. Construction 3. Chemical Industry (plus the first 10%) 4. Services 5. Machinery 6. Other Electronic Equipment 7. Electrical Equipment

The first 25% of sectors

X. Sun et al. / Energy 94 (2016) 195e205

199

Fig. 4. Compositions of energy consumption by top 7 sectors.

central sector if it connects to a key sector with a strong link. This is similar to one person who is always treated as a celebrity if he/she is well-connected with a superstar. In complex network theory, the importance of a node is recursively related to the importance of the nodes pointing to it [40]. This is measured by eigenvector centrality. Applying this measurement to the indirect energy flow data with the software Gephi, we observed that the services sector is the most influential sector in all IEFNs with eigenvector centrality of 1, which means all the sectors connecting to the services sector are important. This consist with the intuition since services sector facilitates the productions of other sectors by offering financial services, technological services, and information services etc. In IEFN-1 and IEFN-2, services is followed by wholesale trade and chemical

industry, while in IEFN-3, services is followed by chemical industry and construction. In the indirect flow network, these sectors are key sectors since their performance on supply and consumption will affected directly the “star” sectors' performance. 3.4. Key sectors in IEFNs based on betweenness centrality In the process of indirect energy flow between sectors, there is one type of sector that mediates between all others. In plain words, a sector is critical if it frequently lies between other sectors [20]. This intuitive notion is captured by betweenness centrality. The betweenness centrality of node k is written according to [41], as shown in Eq. (9):

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XX . gikj gij ; isjsk i

Fig. 5. Sectors' embodied energy coefficients. Note: On the horizontal axis, 1 denotes Agriculture sector, 2 denotes Coal Mining sector, 3 denotes P&G Extraction sector, 4 denotes Metal Mining sector, 5 denotes Nonmetal Mining sector, 6 denotes Food sector, 7 denotes Textile sector, 8 denotes Leather Manufacture sector, 9 denotes Furniture Manufacture sector, 10 denotes Education Related Products sector, 11 denotes Fuel Processing sector, 12 denotes Chemical Industry sector, 13 denotes Non-metallic Products sector, 14 denotes Metals' Smelting sector, 15 denotes Metal Products sector, 16 denotes Machinery sector, 17 denotes Transport Equipment sector, 18 denotes Electrical Equipment sector, 19 denotes Other Electronic Equipment sector, 20 denotes Measuring Machinery sector, 21 denotes Other Manufacturing sector, 22 denotes Electric and Heat Power Production sector, 23 denotes Gas Production sector, 24 denotes Water Production sector, 25 denotes Construction sector, 26 denotes Transport sector, 27 denotes Wholesale Trade sector, 28 denotes Services sector. This note also applies to Figs. 6, 8 and 9.

Fig. 6. Sectors' monetary intermediate inputs.

Fig. 7. Cumulative distribution of weighted-out degree.

(9)

j

where gij is the number of shortest paths between i and j, and gikj is the number of these shortest paths that pass through k. The greater the betweenness centrality, the more central this node is in the IEFN. As shown in Fig. 9, chemical industry, non-metallic products, measuring machinery, other manufacturing, electric and heat power production, and services are more central than other sectors in terms of betweenness centrality. This centrality means that these sectors are a bottleneck of the whole economy by controlling the indirect energy flow between sectors. Shocks to these sectors are likely to lead to breaks in indirect energy flow between upstream sectors and downstream sectors, thus resulting in macroeconomic fluctuations. On the other hand, the sustainable development of these sectors will be helpful in accelerating the indirect energy flow, thus leading to more efficient energy consumption. However, it is worth noting that the bridge strength of one sector is dynamic, especially in IEFN-2 and in IEFN-3, when most sectors experience a decline in betweenness centrality. It is likely to the result of the decline in the number of shortest paths passing through one sector. In other words, this could be explained by increasing mutual connections between sectors. Nevertheless, key sectors in terms of betweenness centrality still exist in the IEFNs. 3.5. Key indirect energy flow paths In addition to the information about network nodes, we also analyze the weighted edges that carry indirect energy flow and thus determine which edges play critical roles in IEFNs. Fig. 10 clearly shows that 20% of the energy flow edges carry approximately 80% of the total indirect energy flow volume. These edges are recognized as key edges in IEFNs. Fig. 10 also shows that the proportion of the indirect energy flow that key edges carrying is higher in IEFN-3 (more than 80%) than that in IEFN-1 and that in IEFN-2. Table 3 shows the details of the indirect energy flow. In IEFN-1, seven edges account for 25.60% of the indirect energy flow in the network: chemical industry to chemical industry, non-metallic products to construction, metals' smelting to metals' smelting, metals' smelting to metal products, metals' smelting to machinery, chemical industry to agriculture, and metals' smelting to electrical equipment. In IEFN-2, the situation is a little different. Seven edges account for 24.20% of the indirect energy flow in the network: chemical industry to chemical industry, metals' smelting to metals' smelting, metals' smelting to construction, non-metallic products to construction, metals' smelting to machinery, other electronic equipment to other electronic equipment, and metals' smelting to metal products. In IEFN-3, we find that metals' smelting to metals' smelting, chemical industry to chemical industry, non-metallic products to construction, metals' smelting to construction, other electronic equipment to other electronic equipment, electric and heat power production to electric and heat power production, and metals' smelting to machinery account for 27.51% of the indirect energy flow in the network. We obtain that the first 0.009% edges account for approximately 25% of the indirect energy flow. These edges are definitely the core edges of the key edges. Based on the above description of results, we find an interesting phenomenon in IEFNs, namely the self-loop. Self-loop means that a sector's indirect energy partially flows back to itself. There are four sectors in the core edges that have this property: the chemical industry, the metals' smelting, the other electronic equipment, and the electric and heat power production (see Table 3). This property

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Table 2 Results of weighted out-degree. Period

1993e1997

1998e2002

2003e2007

The first 10% of sectors

1. Chemical Industry 2. Metals' Smelting 3. Non-metallic Products (plus the first 10%) 4. Electric and Heat Power Production 5. Agriculture 6. Metal Products 7. Fuel Processing

1. Metals' Smelting 2. Chemical Industry 3. Transport (plus the first 10%) 4. Non-metallic Products 5. Fuel Processing 6. Electric and Heat Power Production 7. Services

1. Metals' Smelting 2. Chemical Industry 3. Electric and Heat Power Production (plus the first 10%) 4. Non-metallic Products 5. Fuel Processing 6. Transport 7. Machinery

The first 25% of sectors

Fig. 8. Sectors' intermediate monetary outputs.

clearly shows the difference between indirect energy and direct energy. For instance, in IEFN-3, the chemical industry outputs a total 88,102.03 Mtce and inputs a total of 60,929.60 Mtce; the chemical industry outputs to itself 36,945.41 Mtce, which accounts for 41.93% (i.e. 36,945.41/88,102.03) of the indirect energy output and 60.64% (i.e. 36,945.41/60,929.60) of the indirect energy input. For metals' smelting, the two proportions are 33.40% and 55.80%, respectively. For the other electronic equipment, the two proportions are 73.80% and 55.04%, respectively. For the electric and heat power production, the two proportions are 37.25% and 57.16%,

Fig. 9. Sectors' betweenness centralities.

respectively. The difference between the former proportion and the later one lies in the fact that denominator is different. The former denominator is the weighted out-degree while the later denominator is the weighted in-degree. For the former proportion, we calculate it as the indirect energy output to itself (oii ) to the total indirect energy output (Oi Þ; while the later one is the ratio between oii and the total indirect energy input (Ii ). The former proportion measures the contributions made by this sector to the other sectors and the later one measures the self-dependency degree in terms of indirect energy. In addition, we determined key indirect energy flow paths in the IEFNs as follows. First, we selected the edges carrying the first 25% of the indirect energy flow and ranked them according to their carrying volume. Second, we set the source sector of the first edge as the starting sector of the first key indirect energy flow path and linked the source sector to the sector that it supplies most (besides itself). Then, we linked the second sector to a third sector that it supplies most (besides itself). This process continues until the last sector turns back to the second last sector. In IEFN-1, there were three key paths: (1) chemical industry to agriculture to food; (2) non-metallic products to construction to services to wholesale trade; and (3) metals' smelting to metal products to construction to services to wholesale trade. In IEFN-2, there were four key paths: (1) chemical industry to agriculture to food to wholesale trade; (2) metals' smelting to construction to services to wholesale trade; (3) non-metallic products to construction to services to wholesale trade; and (4) other electronic equipment to services to wholesale trade. In IEFN-3, there were five key paths: (1) metals' smelting to construction to services to wholesale trade; (2) chemical industry

Fig. 10. Cumulative distribution of weighted edges.

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Table 3 Results of the first 25% of the total indirect energy flow.

Source (code) Chemical Industry (S1) Non-metallic Products (S2)

1993-1997

Target (code) Chemical Industry (T1) Construction (T2) Metal Products (T4) Machinery (T5)

Chemical Industry (S6)

Agriculture (T6) Electrical Equipment (T7)

Chemical Industry (S1)

Chemical Industry (T1) Construction (T3)

1998-2002

Non-metallic Products (S4)

Construction (T4) Machinery (T5)

Other Electronic Equipment (S6)

Other Electronic Equipment (T6) Metal Products (T7)

Chemical Industry (S2) Non-metallic Products (S3)

2003-2007

Chemical Industry (T2) Construction (T3) Construction (T4)

Other Electronic Equipment (S5) Electric and Heat Power Production (S6)

Other Electronic Equipment (T5) Electric and Heat Power Production (T6) Machinery (T7)

Note: Si denotes the ith source sector, and Ti denotes the ith target sector to which the ith source sector flows. For example, the link chemical Industry flows to chemical Industry is denoted as S1 to T1.

to services to wholesale trade; (3) non-metallic products to construction to services to wholesale trade; (4) other electronic equipment to services to wholesale trade; and (5) electric and heat power production to chemical industry to services to wholesale trade. From the results above, we can see that the number of key paths is increasing, which indicates an increasingly balanced diverse economic structure in China.

Firstly, based on the results of degree centrality, sectors with large weighted degrees are treated as key sectors (see Fig. 11). It is easy to understand that this kind of key sectors have huge indirect energy flow volume and thus the total flow volume may be affected when these sectors are intervened in the process of policy makings.

4. Discussions and policy implications The indirect energy flow network displays the small world nature, which means the economic relations between sectors are very close and effects on one sector may spread very quickly to other sectors in the indirect energy flow network. The clustering coefficient increases from 0.955 to 0.97 and the average path length declines from 1.045 to 1.03 from 1993 to 2007, which shows that the economic relations between sectors becomes more and more closer and the spread becomes easier. This result provides information for policy making that the indirect energy network becomes more sensitive to changes of sectors, especially the changes of key sectors may result in a systemic effect on indirect energy flow network. Different sectors play various roles in the indirect energy flow network. And we have identified key sectors from three perspectives. These identifications provide valuable information for policy makings.

Fig. 11. Key sector based on degree centrality. Note: The size of the node denotes the value of the centrality. The bigger it is, the larger the value is. The thickness of line denotes the volume of indirect energy flow. This note also applies to Figs. 12 and 13.

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Fig. 12. Key sector based on eigenvector centrality.

Secondly, eigenvector centrality is different from the degree centrality (see Fig. 12). On the basis of eigenvector centrality, this kind of key sectors probably does not have huge indirect energy flow volume, as the key sectors defined by degree centrality do. However, the sectors with large eigenvector centralities connect with the sectors with huge indirect energy flow volumes. This result provides the information that the interventions on this kind of sectors are likely to have indirect effects on the sectors with huge indirect energy flow volume and thus achieve the relevant policy goals. Thirdly, betweenness centrality measures the bridge effect in the indirect energy flow network (see Fig. 13). This kind of sectors play the media roles in the network. Similar to controlling the spread of a virus, we should not only control the source of the virus but also stop the transmission by controlling the medium. On one hand, through the adjustments of this media sectors is it helpful to contain the spread of negative effects (such as air pollutions). On the other hand, the benefits can be obtained through the incentives to these media sectors. Moreover, besides the perspective of sectors, policy makers may get useful information from the perspective of edges connecting sectors. Based on the analysis of key paths, we observe that 20% of the energy flow edges carry approximately 80% of the total indirect energy flow volume. This informs the policy makers of not only paying attention to key sectors but also emphasizing the key indirect energy flow paths. In addition, the interventions of few key flow paths will cover the majority of indirect energy flow and thus make the policy makings more oriented.

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IEFNs with 28 sectors based on InputeOutput tables from 1997, 2002, and 2007. Results show that IEFNs present the small world nature, which means indirect energy flow between sectors is sensitive to disturbance. The various roles of the sectors played in the IEFNs are captured by three centrality indicators, namely degree centrality, eigenvector centrality, and betweenness centrality. And the sectors with large values in these three centrality indicators are recognized as key sectors. The resultant coreperiphery structure is presented. This structure does not change but the sectors in the key positions do. In addition, we analyzed the indirect energy flow paths in the network and identified key flow paths. 20% of the energy flow edges carry approximately 80% of the total indirect energy flow. Self-loop in the IEFNs also analyzed. Identifying the specific roles of sectors and key indirect energy flow paths in the IEFNs, we discussed the policy implications based on the different positions of sectors in the indirect energy flow network.

Acknowledgments We acknowledge the National Natural Science Foundation of China (Grant No. 71173199) and Fundamental Research Funds for the Central Universities (Grant No. 53200859403) for financial supports, and are grateful for the helpful comments of those who attended weekly seminars at the School of Humanities and Economic Management in China University of Geosciences, Beijing. We also appreciate deeply the three anonymous referees who gave us insightful remarks and useful suggestions to improve substantially the manuscript.

Appendix A In this study, we consolidate sectors in an energy balance sheet and IeO table for different periods into a 28-sector energy IeO table (see Table A.1).

Appendix B

Table A.1 Industrial sectors classification.

5. Conclusion This study revealed the structure of indirect energy flow network and its trend from 1993 to 2007 by constructing three

Final classification (Sector code)

Sub-sectors (Sector code)

Agriculture (1)

Farming (1-01) Forestry (1-02) Animal Husbandry (1-03) Fishery (1-04) Water Conservancy (1-05) Mining and Washing of Coal (2-01) Extraction of Petroleum and Natural Gas (3-01)

Coal Mining (2) Petroleum and Gas Extraction (3) Metal Ores Mining (4)

Nonmetal Ores and Other Mining (5) Food Manufacture (6)

Mining and Processing of Ferrous Metal Ores (4-01) Mining and Processing of Non-Ferrous Metal Ores (4-02) Mining and Processing of Nonmetal Ores (5-01) Mining of Other Resources (5-02) Processing of Food from Agricultural Products (601) Manufacture of Foods (6-02) Manufacture of Beverages (6-03) Manufacture of Tobacco (6-04) (continued on next page)

Fig. 13. Key sector based on betweenness centrality.

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Table A.1 (continued ) Final classification (Sector code)

Sub-sectors (Sector code)

Textile Manufacture (7) Textile Wearing and Leather Manufacture (8)

Manufacture of Textile (7-01) Manufacture of Textile Wearing Apparel, Footwear, and Caps (8-01) Manufacture of Leather, Fur, Feather and Related Products (8-02) Processing of Timber, Manufacture of Wood, Bamboo, Rattan, Palm, and Straw Products (9-01) Manufacture of Furniture (9-02) Manufacture of Paper and Paper Products (10-01) Printing, Reproduction of Recording Media (10-02) Manufacture of Articles For Culture, Education and Sport Activity (10-03) Processing of Petroleum, Coking, Processing of Nuclear Fuel (11-01)

Timber Processing and Furniture Manufacture (9) Manufacture of Paper and Education related products (10) Petroleum Processing, Coking, and Nuclear Fuel (11) Chemical Industry (12)

Manufacture of Nonmetallic Mineral Products (13) Smelting and Pressing of Metals (14) Manufacture of Metal Products (15) Manufacture of General and Special Purpose Machinery (16) Manufacture of Transport Equipment (17) Manufacture of Electrical Machinery and Equipment (18) Manufacture of Communication Equipment, Computers and Other Electronic Equipment (19) Manufacture of Measuring Instruments and Machinery (20) Other Manufacturing (21) Production and Distribution of Electric Power and Heat Power (22) Production and Distribution of Gas (23) Production and Distribution of Water (24) Construction (25) Transport, Storage and Post (26) Wholesale, Retail Trade and Hotel, Restaurants (27) Services (28)

Manufacture of Raw Chemical Materials and Chemical Products (12-01) Manufacture of Medicines (12-02) Manufacture of Chemical Fibers (12-03) Manufacture of Rubber (12-04) Manufacture of Plastics (12-05) Manufacture of Non-metallic Mineral Products (1301)

Table A.2 Industrial sectors' abbreviations. Abbreviations

Full name of Industrial sectors

Agriculture Coal Mining P&G Extraction Metal Mining Nonmetal Mining Food Textile Leather Manufacture Furniture Manufacture Education Related Products

Agriculture Coal Mining Petroleum and Gas Extraction Metal Ores Mining Nonmetal Ores and Other Mining Food Manufacture Textile Manufacture Textile Wearing and Leather Manufacture Timber Processing and Furniture Manufacture Manufacture of Paper and Education Related Products Petroleum Processing, Coking, and Nuclear Fuel Chemical Industry Manufacture of Non-metallic Mineral Products Smelting and Pressing of Metals Manufacture of Metal Products Manufacture of General and Special Purpose Machinery Manufacture of Transport Equipment Manufacture of Electrical Machinery and Equipment Manufacture of Communication Equipment, Computers and Other Electronic Equipment Manufacture of Measuring Instruments and Machinery Other Manufacturing Production and Distribution of Electric Power and Heat Power Production and Distribution of Gas Production and Distribution of Water Construction Transport, Storage and Post Wholesale, Retail Trade and Hotel, Restaurants Services

Fuel Processing Chemical Industry Non-metallic Products Metals' Smelting Metal Products Machinery Transport Equipment Electrical Equipment Other Electronic Equipment Measuring Machinery

Smelting and Pressing of Ferrous Metals (14-01) Smelting and Pressing of Non-ferrous Metals (1402) Manufacture of Metal Products (15-01) Manufacture of General Purpose Machinery (16-01) Manufacture of Special Purpose Machinery (16-02) Manufacture of Transport Equipment (17-01)

Other Manufacturing Electric and Heat Power Production Gas Production Water Production Construction Transport Wholesale Trade Services

Manufacture of Electrical Machinery and Equipment (18-01) Manufacture of Communication Equipment, Computers and Other Electronic Equipment (19-01)

Table B.1 In-degrees and out-degrees of sectors. Sector 1993e1997

Manufacture of Measuring Instruments and Machinery for Cultural Activity and Office Work (20-01) Manufacture of Artwork and Other Manufacturing (21-01) Recycling and Disposal of Waste (21-02) Production and Distribution of Electric Power and Heat Power (22-01)

Production and Distribution of Gas (23-01)

Production and Distribution of Water (24-01)

Construction (25-01) Transport, Storage (26-01) Post (26-02) Wholesale, Retail Trade and Hotel, Restaurants (27-01) Information, Transmission, Computer Services & Software (28-01) Real Estate, Leasing and Business Services (28-02) Financial Intermediation (28-03) Other Services (28-04)

1998e2002

2003e2007

In-degree Out-degree In-degree Out-degree In-degree Out-degree 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

26 27 27 28 26 27 27 26 26 27 26 28 28 27 27 27 27 27 28 27 26 27 27 28 26 27 25 25

24 28 25 13 28 17 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 27 28

27 27 27 28 26 27 26 25 25 27 25 28 28 27 27 27 27 27 27 28 28 27 25 26 26 27 26 28

28 28 25 13 22 17 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28

27 27 27 28 27 27 26 26 26 26 27 28 28 28 28 28 28 28 28 28 28 27 26 27 26 28 27 26

26 28 27 13 23 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28

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