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The community structure identification for the Chinese merger and acquisition network
Physica A 526 (2019) 120897
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Physica A journal homepage: www.elsevier.com/locate/physa
The community structure identification for the Chinese merger and acquisition network Xin-Yu Guo a , Kai Yang b , Xian-Ming Wu a , Qiang Guo b ,
∗
a
Economics and Management School, Wuhan University, Wuhan 430072, PR China
b
Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China
highlights • The community structure of the Chinese mergers and acquisitions companies is investigated from the viewpoint of macroscopic level.
• The network has the clear community structures with the modularity Q=0.8757. • There are a large proportion of companies belonging to one industry for each community. • The number of triangular configuration is very few.
article
info
Article history: Received 6 January 2019 Received in revised form 24 February 2019 Available online 8 April 2019 Keywords: Mergers and acquisitions Complex networks Directed networks Community structure
a b s t r a c t The community structures of the mergers and acquisitions (M&As) could bring deeply insight on the company complex system from the viewpoint of macroscopic level. Firstly, we construct the directed merger and acquisition network (MAN) based on the M&A events which deal from 2000 to 2017 initiated by Chinese listed companies, where the nodes represent the companies and the links denote the relationship of M&As. Regarding the fact that the M&A network is a directed network, by using the Infomap algorithm, we investigate the community structures of the M&A network, and find that the network has the clear community structures with the modularity Q = 0.8757. Furthermore, we present a parameter η defined as the ratio of the number of companies which belong to the same industry to the total number of companies in the community for analyzing the company industry characteristics within community. The empirical results show that there are a large proportion of companies belonging to one industry for each community, which illustrates that the characteristic of M&As is that M&As generally occur between the same industry within communities. Finally, we calculate the clustering coefficient of directed networks to analyze the clustering properties of the network with the community structures. The clustering coefficient of the network indicates that the number of triangular configuration is very few, which illustrates that the relationship of a company’s neighbors is weak. This work provides insight to structural properties of directed networks based on the M&As from the perspective of complex systems. © 2019 Elsevier B.V. All rights reserved.
∗ Corresponding author. E-mail address: [email protected] (Q. Guo). https://doi.org/10.1016/j.physa.2019.04.133 0378-4371/© 2019 Elsevier B.V. All rights reserved.
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1. Introduction Mergers and acquisitions (M&As) [1–5] are among the most important investment decisions made by a company, given their strategic nature and the long-term impact such decisions have on the operational and financial restructuring of the company. Existing literature has evolved extensively over the last few decades with the result that a number of theories on M&As have been proposed and empirically tested. Hoberg and Phillips [6] pinpointed product market synergy as important drivers of M&As, and contributes to a broader literature on asset complementarity and mergers [7]. Fan and Goyal [8] demonstrated the importance of vertical relatedness of firms’ industries for merger outcomes. Ahern and Harford [9] argued that both intra- and interindustry merger waves are driven by customer–supplier relations between industries. In recent years, researchers have begun to focus their interests on corporate control activity in emerging markets, in particular China. Chinese listed firms have gained the world’s attention with several ambitious, high-profile crossborder mergers and acquisitions. Chen et al. [10] found that investors are indeed skeptical of cross-border mergers and acquisitions deals when the government is the majority owner (i.e., principal–principal conflicts) by investigating a sample of cross-border mergers and acquisitions involving Chinese firms from 2000 to 2008. Bhabra et al. [11] examined 136 M&A deals from 1997 to 2007 initiated by Chinese companies listed on the Shanghai and Shenzhen Stock Exchanges. They showed that the Chinese M&A market is dominated by domestic deals with unlisted targets that are either standalone private firms or wholly owned subsidiaries. Cross-sectional tests showed that announcement period returns are related to the acquirer’s ownership status, industry relatedness of the acquirer and target, capital structure changes of the acquirer and the nature of the unlisted target. And they found no change in operating performance from the pre to the post acquisition period for the acquirers. Complex networks have been widely used in science and technology because of their ability to represent several systems [12–15]. Within the framework of a complex network perspective, an increasing body of literature has been studying M&As. Havila et al. [16] investigated the spread of change in business networks with focus on critical events as triggers of radical change. They found that M&As may cause changes that spread in the business networks, and M&As are investigated as triggers of radical network change in particular. Öberg et al. [17] used the concepts of ‘network pictures’ [18] and ‘networking’ to illustrate and analyze changes in managerial sense-making and networking activities following a merger or acquisition. They showed that following a merger or acquisition managers may need to adapt their previous network pictures in a radical way; these adaptations are, however, not always realized as shifts in ¨ network pictures and adjustments in networking activities by all the managers involved. Duenas et al. [19] analyzed the world web of M&As using a complex network approach. In contrast to the international trade network (ITN), they found that international M&A network was characterized by a persistent giant component with many external nodes and low reciprocity. Clustering patterns were very heterogeneous and dynamic. Many networks exhibit the property of containing community structure [20,21], which has attracted much attention in the past several decades [22–25]. However, they did not analyze the community structures of company’s merger and acquisition networks and network structure characteristics of listed companies for M&As from the perspective of macroscopic level. Inspired by above ideas, we detect community structures of M&A network (MAN) and analyze the properties of mergers and acquisitions for Chinese listed companies in this paper. Firstly, we construct temporal directed networks by preprocessing the data set with Chinese listed companies’ M&A events from 2000 to 2017, where the nodes are the companies, the links represent flows for the M&As, and analyze the evolution properties of the M&A data. Then, we detect the community structure [26–29] of the largest connected component for MAN using Infomap algorithm to investigate the structural properties of MAN. Then, we calculate the modularity of directed networks to evaluate the performance of the community structures. The result shows that the network has clear community structures with the modularity Q = 0.8757. Furthermore, we introduce a parameter η to investigate the industry characteristics for each community. The empirical results indicate that there are a large percentage of companies belonging to the same industry for each community we list. Finally, we further analyze the clustering of the network with community structures, and find that the number of triangle configuration is few, which illustrates that the relationship of a company’s neighbors is weak by calculating the clustering coefficient of the largest connected component. 2. Model and methods In this section, we introduce the model and methods used in this paper. Based on the network science, we investigate the Chinese listed company mergers and acquisitions. The Chinese company M&A network is constructed, which is introduced in the following. 2.1. The construction of network Using the data collected by this paper, we can define the directed M&A network (MAN) in its binary representation. The network at a given point of time t is represented by a directed network, where the nodes are the companies linked by M&A flows, the number is N(t) and links are fully characterized by the N(t) × N(t) asymmetric matrix A(t), with
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entries aij (t) =1 if M&As flows from company i to company j are strictly positive, i.e. a flow of M&As from company i to company j. In order to investigate the characteristics of all the M&A events we collected, we integrated the networks at all times and merged them into a whole network G = (V , E), where V , E are the sets of nodes and links of the network respectively, denotes as MAN. Finally, we extract the largest connected component (LCC) to illustrate the structural properties for M&As. In a network, the mean path length is the average shortest path between two nodes. In this paper, we consider the network as an undirected network when calculating the shortest path. Let dij be the length of the shortest path between nodes i and j. The mean path length is the average of the shortest path length, averaged over all pairs of nodes. For an undirected network of n nodes, the mean path length L is L=
1
∑
n(n − 1)
dij ,
(1)
i̸ =j
where the sum is over all pairs of distinct nodes. The diameter D of the network is the maximum of the shortest path length between two nodes. If two nodes are disconnected, meaning there is no path between them, then the path length between them is infinite. As a consequence, if a network contains disconnected components (collections of nodes that have no paths between them), then the mean path length L also diverges to infinity. One possibility to avoid the divergence is to limit the summation in formula (2) only to couples of nodes belonging to the largest connected component [30]. An alternative approach, that is useful in many cases, is to consider the harmonic mean [31] of geodesic lengths, and to define the so-called efficiency ℓ of G as ∑ 1 1 ℓ= , (2) n(n − 1) dij i̸ =j
The density Den of a network containing n nodes is defined as the ratio of the number of links m actually present in the network to the maximum possible number of links. m Den = , (3) n(n − 1) Network clustering is a well-known concept in complex networks, clustering coefficient can be measured by the percentage of pairs of i’s neighbors that are themselves neighbors, i.e. by the ratio between the number of triangles in the network G with i as one node and the number of all possible triangles that i could have formed. In directed networks, links are oriented and neighboring relations are not necessarily symmetric. The clustering coefficient for node i (CCi ) in directed networks [32] can be thus defined as the ratio between all directed triangles actually formed by i (labeled as tDi ) and the number of all possible triangles that i could form (labeled as TDi ). CCi =
tDi TDi
.
(4)
Degree correlation [33] describes the relationship between the degrees of nodes that link to each other and could reveal the network topology which belongs to assortative network, disassortative network or neutral network. Since nodes in directed networks have both an in-degree and an out-degree, we introduce a set of four directed assortativity measures. β Let α, β ∈ {in, out } index the degree type, and dαl and kl be the α− and β−degree of the source node and target node for link l. Then, the set of assortativity measures using Pearson correlation is defined as follows, r(α,β ) =
m−1
∑
l
β
[(dαl − dα )(kl − kβ )] , σ ασ β
(5)
√
where m is the number of links in the network, dα = m−1 l dαl , and σ α = m−1 l (dαl − dα )2 , and kβ and σ β are similarly defined. In each correlation the links point from the node with the α−indexed degree to the node with the β−indexed degree. Classes of directed networks show common patterns across the four directed assortativity measures: r(in,out) , r(in,in) , r(out ,in) , r(out ,out) . The first element in the parentheses labels the degree of the source node of the directed link, and the second labels the degree of the target node. Thus r(in,out) quantifies the tendency of nodes with high in-degree to connect to nodes with high out-degree, and so on.
∑
∑
2.2. The community structure detection In order to investigate the structural patterns of Chinese listed company mergers and acquisitions, we have detected the community structure of the largest connected component of the M&A network. The method we use in this paper is the classic community structure detection algorithm (Infomap algorithm) on the directed network. Rosvall and Bergstrom [34] proposed a method (called Infomap) to identify communities in directed networks, by combining random walks and compression principles. That is, the modules of the network can be recognized based on how fast information flows on them. The authors apply the concept of random walks to describe the process of information
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X.-Y. Guo, K. Yang, X.-M. Wu et al. / Physica A 526 (2019) 120897 Table 1 The evolution properties of the M&A data. Ncom is the number of companies related to M&As, Nma represents the number of M&A events. Nc denotes the number of connected components for the data sets. Ncom Nma Targets(No.) Acquires(No.) Nc
2000
2005
2010
2015
2017
294 182 141 153 112
2022 1330 1004 1018 714
2112 1366 1004 1151 772
2786 1872 1069 1717 932
3673 2325 1554 2129 1362
flow in the network and the clusters can be extracted by compressing the description of the random walk. A community corresponds to a group of nodes in which the random surfer is more likely to be trapped in, visiting more time nodes of the group than other nodes outside of that. Thus, intuitively, a community would correspond to a group of nodes in which the random walk can be compressed better and the problem can be reformulated as a coding one: the goal is to select a partition M of the n nodes into c communities, minimizing the description length of the random walk. At the first step, each node in the network is described by a unique codeword based on the visiting frequency of the random walk. Using Huffman coding, shorter codewords are assigned to more frequently visited nodes. At the second step, the random walk trajectory on the network can be described following a two-level description: unique names (codewords) are assigned to the clusters of the network (coarse-grained structure), while the codewords for the description of nodes inside a module are reused (fine-grained structure). Thus, reporting only the codewords that have been assigned to communities, a coarse grained description of the network is achieved. The procedure is similar to the one used while designing a geographic map; unique names are assigned to cities (communities in our case), while names for the streets (nodes in our case) of a city can be reused. Then, the clustering problem can be expressed as finding the partition that yields the minimum description code length. If the network has a well-defined community structure, the above twolevel description scheme will produce shorter code length: the random walk will jump between different communities infrequently and thus the description length will be shorter (since the codewords represent individual nodes are shorter). The minimization of the description length can be achieved combining greedy search and simulated annealing methods. Furthermore, we use the modularity function Q [35] as the standard to evaluate the performance of Infomap algorithm. The function can be defined as follows: Q =
1 ∑ m
[Aij −
ij
out kin i kj
m
]δci ,cj .
(6)
where δci ,cj = 1 if the community assignments ci and cj of nodes i and j are the same and 0 otherwise. 3. The experimental analysis 3.1. Data set In this paper, the data we used for the analysis is extracted from Choice financial terminal. It is a financial big data platform owned by Orient Wealth, which covers information on market data of multiple investment types, has a convenient data browser and thematic design, and assists investors in data extraction, analysis and all-round research. We collect the data set which is the Chinese listed company’s M&A events covering the period from 2000 to 2017. The recorded transactions (in volume) referring to M&A activity include the name of the listed companies, the properties of companies, the industries that the companies belong to, the time when the transaction was closed, and the purchase amount of money for M&As and other information. We preprocess the data set, remove the invalid records and the data that do not meet the conditions. 3.2. Statistical properties of the M&A data Firstly, we extract the basic information of the data set we collected. The evolution properties of the M&As for Chinese listed companies in different years are shown in Table 1. We distinguish between acquirers, companies merge or acquire other companies, and targets, companies merged and acquired by other companies. Table 1 shows the number of the listed companies which related to M&As and the number of M&A events from 2000 to 2017. The number of acquirers/targets making up a high percentage (50%) to/from targets/acquires is very concentrated, although it slightly increases over time, which may indicate a spread of acquirers to new markets. As can be seen from the table, the number of companies that related to the M&As and the Chinese listed company M&As has growth trend. The number of the connected components, as a proportion of the number of companies in the network in a given year, reaches up to 37%, which indicates M&A relations are generally unilateral. Then, we analyze the properties and industries of the companies for the listed company M&As in each year. As there are many companies which are not given the properties of the company in the data set, we only analyze the M&A events in
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Fig. 1. The number of companies for different properties and industries in mergers and acquisitions from 2000 to 2017. We can find that the number of state-owned enterprises is larger than the others before 2014, however, the number of private enterprises has occupied the first place, exceeding the number of state-owned enterprises after 2014. Meanwhile, the proportion of the real estate industry has decline trend, and the proportion of industrial machinery and group companies has increased from 2014.
which the companies are given the properties of the company. The results are shown in Fig. 1. As can be seen from Fig. 1(a), the state-owned enterprises and private enterprises account for a relatively large proportion of the listed company M&A events in each year. In particular, the number of state-owned enterprises was larger than that of private enterprises from 2000 to 2013, however, the number of private enterprises has surpassed that of state-owned enterprises from 2014. As there are many industry categories of companies in the data set, and the number of companies in many industries is few, we investigate the evolutions of the industries which listed the top five company industries in 2017. Similarly, we only analyze the companies which labeled the industries in the data set. The result is shown in Fig. 1(b). We can find that the number of companies belonging to real estate industry has been relatively large before 2013, which indicates the real estate industry is active in the market. However, the proportion of the number of companies in industrial machinery and group companies, chemicals and pharmaceuticals, electronic equipment and other industries surpassed the real estate industry after 2014, indicating that the real estate industry gradually has been stable in the market, while other industry companies have been adjusted. Finally, we build the temporal directed M&A networks at each time based on the data set. In order to further analyze properties of M&As from a global perspective, we have integrated the networks from 2000 to 2017 to a whole network, denote as MAN. There are 21,885 nodes, and the number of connected components is 3669, which shows that most of nodes are disconnected with each other in the MAN. The density of the MAN is 4.04 × 10−5 , which indicates the MAN is a low density network. In addition, we also calculate the network’s efficiency ℓ, which is 0.01147, as the network is disconnected. This illustrates that the possibility of reaching nodes with each other in the network is small, which means that the network is sparse. Furthermore, the number of nodes of which out-degree is 1 accounts for 70.3%, and the percentage of the number nodes of which in-degree is equal to 1 is 82.6%, which indicates that a company generally acquires one company, and a company is generally only acquired by one company. 3.3. The community structures of the MAN In order to investigate the structural properties of the integrated network, we extract the largest connected component from MAN and further analyze the network structural patterns for the M&As. Firstly, we investigate the basic structural properties of the largest connected component, analyze the basic structural properties of largest connected component. The results show that the number of nodes and links of the largest connected component are 8030, 8836 respectively, and the density of the largest connected component is 1.37×10−4 , which indicates the largest connected component is a low density network. The average shortest path length L of the largest connected component is 13.487 and the diameter D is 45, which illustrates that the average path length where the nodes in the network reach with each other is very long and the nodes have a weak connected relationship with each other. Then, we analyze the macroscopic structural properties by identifying the community structures of directed connected component using the Infomap algorithm and the result shows that the directed connected component is divided into 17 communities. We calculate the modularity Q of the directed network after detecting the community structure to measure the accuracy of the community structure. The modularity Q = 0.8757 indicates that the Infomap algorithm well detect the community structure in the directed M&A network, and the M&A network also has clear community structure. We further investigate the company industries within the community to analyze the characteristics of community structure. We calculate the proportion of companies belonging to the same industry in top seven size communities (The number of nodes in top seven communities accounts for 72.7% of total nodes in the all communities). The proportion of the top three industries of companies in each community is given as shown in Table 2. The ratio η describes the proportion of the number of companies labeled the same industry to the total number of companies within
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X.-Y. Guo, K. Yang, X.-M. Wu et al. / Physica A 526 (2019) 120897 Table 2 The proportion of the company’s industry in the top seven communities. The ratio η is the proportion of the number of companies which belong to a same industry to the total number of companies in the community. Label
The industries
η (%)
1
Architecture and engineering Real estate development Industrial group enterprise
8.25 5.71 4.02
2
Electric utility Pharmaceutical Industrial group enterprise
12.35 5.98 5.98
3
Aerospace and Defense Real estate development Asset Management and Escrow Bank
7.51 5.78 5.20
4
Electric utility Real estate development Sea transportation
8.45 7.75 7.04
5
Real estate development Steel Trading company and distributor
8.18 6.92 5.66
6
Investment banking and brokerage Industrial group enterprise Real estate development
8.61 6.62 5.96
7
Real estate development Coal and consumer fuel Building materials
8.11 6.76 5.41
a community. As there are many industry categories in each community, the average number of industry categories for the top seven size community is 60, and there are even 103 industry categories in the largest size community, thus the proportion of industries for each community is relatively small. From Table 2, one can find that the first-ranked industries in each community are different, except for the fifth and seventh communities. It indicates that most of the companies in a community belong to the same industry. In details, the number of companies belonging to architecture and engineering accounts for 8.25% in the largest size community. It illustrates that the industry labeled the companies in the community mainly relate to the architecture and engineering. For other communities, the same conclusion can be drawn. These results show that the listed company M&As generally occur between the same industry. In addition, we also find that the real estate industry has a large proportion in each community, which indicates that the real estate industry is closely related to other industries. To investigate the clustering of the network with community structure, we calculate the clustering coefficients of the directed network. For directed networks, there are four different patterns of directed triangles that result in four different clustering coefficients in Fig. 2(a). We can see that overall these four clustering coefficients are small and close to zero, which exhibits that the number of triangle configuration in the network is very few. To some extent these kinds of triangles describe the partnership of an company’s neighbors. We find that it is difficult for a company to have a merger relationship with two other companies with mergers and acquisitions. This also determines the special network structure configuration of the company M&A network. We also calculate the four kinds of degree correlation coefficients which quantify the assortative or disassortative tendency of the network shown in Fig. 2(b). The values of r(in,out) correlation coefficient and r(in,in) correlation coefficient are close to zero, which reveals no significant correlation between the in-degree for the source nodes and out-degree or in-degree for the target nodes. However, the r(out ,out) correlation coefficient is −0.1510 and r(out ,in) correlation coefficient is -0.1562. They both show significant negative correlation, which indicates that the companies which have plenty of M&A behaviors tend to merge the companies that have not acquired other companies or not been acquired by other companies. 4. Conclusion and discussions In this paper, we empirically investigate the community structure for Chinese listed company M&As from the viewpoint of network science. Firstly, for the case study for listed company M&A behaviors, it is hard to know the evolution of each industry and the properties of companies of M&As behaviors, which handles the risk and importance analyses from the company M&A complex system. Secondly, the listed company M&As behavior is dynamic and directed, which could bring insight for the theoretical development of network science. We detected the community structure of the largest connected component for MAN using the Infomap algorithm to investigate the structural properties of the M&As. The results showed that the network has clear community structure with modularity Q = 0.8757. By the analysis of the company industries in each community, we found that the M&As generally occurred between the same industry for each community. Finally, the clustering coefficient of the directed network with community structures was calculated. The empirical results indicated
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Fig. 2. The four clustering coefficients with eight different directed triangles and the four degree–degree correlations in directed M&A network. From which, we can find that overall these four clustering coefficients are much small, and the absolute value of the coefficient r(out ,out) and r(out ,in) are relatively large.
that the number of triangular configuration in the network is few, which illustrates that the relationship of a company’s neighbors is weak. We investigated the community structure of M&As with complex networks, the following points should be addressed in the future work. Although we have presented various characteristics of the M&A network and drawn some conclusions, we did not analyze the relationship between the performance of M&As and the network structure, and not analyze the changes of organizational structure, customer relationship, management and other aspects of the companies before and after the M&A. Secondly, a lot of companies’ information in the original data is not given, such as the properties of the company or the industries, so we will inevitably have deviations for the statistical analysis of the data set. In addition, the empirical analysis in this paper consists mostly of domestic deals. As cross-border deals grow and public targets come into play, future research should examine the whole patterns of acquisition activity in this rapidly transforming market. Overall, our analysis attempted to provide a network characterization of the MAN that can contribute to future research on international networks. Acknowledgments This work is partially supported by the National Natural Science Foundation of China (Grant No. 61773248, 71771152), and the National Social Science Foundation of China (18ZDA088). References [1] J. Bena, K. Li, Corporate innovations and mergers and acquisitions, J. Finance 69 (5) (2014) 1923–1960. [2] P. Deng, M. Yang, Cross-border mergers and acquisitions by emerging market firms: A comparative investigation, Int. Bus. Rev. 24 (1) (2015) 157–172. [3] S. Rossi, P.F. Volpin, Cross-country determinants of mergers and acquisitions, J. Financ. Econ. 74 (2) (2004) 277–304. [4] I.R.P. Cuypers, Y. Cuypers, X. Martin, When the target may know better: Effects of experience and information asymmetries on value from mergers and acquisitions, Strateg. Manage. J. 38 (3) (2017) 609–625. [5] I. Erel, R.C. Liao, M.S. Weisbach, Determinants of cross-border mergers and acquisitions, J. Finance 67 (3) (2012) 1045–1082. [6] G. Hoberg, G. Phillips, Product market synergies and competition in mergers and acquisitions: A text-based analysis, Rev. Financ. Stud. 23 (10) (2010) 3773–3811. [7] M. Rhodes-Kropf, D.T. Robinson, The market for mergers and the boundaries of the firm, J. Finance 63 (3) (2008) 1169–1211. [8] J.P.H. Fan, V.K. Goyal, On the patterns and wealth effects of vertical mergers, J. Bus. 79 (2) (2006) 877–902. [9] K.R. Ahern, J. Harford, The importance of industry links in merger waves, J. Finance 69 (2) (2014) 527–576. [10] Y.Y. Chen, M.N. Young, Cross-border mergers and acquisitions by Chinese listed companies: A principal–principal perspective, Asia Pac. J. Manag. 27 (3) (2010) 523–539.
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Physica A journal homepage: www.elsevier.com/locate/physa
The community structure identification for the Chinese merger and acquisition network Xin-Yu Guo a , Kai Yang b , Xian-Ming Wu a , Qiang Guo b ,
∗
a
Economics and Management School, Wuhan University, Wuhan 430072, PR China
b
Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China
highlights • The community structure of the Chinese mergers and acquisitions companies is investigated from the viewpoint of macroscopic level.
• The network has the clear community structures with the modularity Q=0.8757. • There are a large proportion of companies belonging to one industry for each community. • The number of triangular configuration is very few.
article
info
Article history: Received 6 January 2019 Received in revised form 24 February 2019 Available online 8 April 2019 Keywords: Mergers and acquisitions Complex networks Directed networks Community structure
a b s t r a c t The community structures of the mergers and acquisitions (M&As) could bring deeply insight on the company complex system from the viewpoint of macroscopic level. Firstly, we construct the directed merger and acquisition network (MAN) based on the M&A events which deal from 2000 to 2017 initiated by Chinese listed companies, where the nodes represent the companies and the links denote the relationship of M&As. Regarding the fact that the M&A network is a directed network, by using the Infomap algorithm, we investigate the community structures of the M&A network, and find that the network has the clear community structures with the modularity Q = 0.8757. Furthermore, we present a parameter η defined as the ratio of the number of companies which belong to the same industry to the total number of companies in the community for analyzing the company industry characteristics within community. The empirical results show that there are a large proportion of companies belonging to one industry for each community, which illustrates that the characteristic of M&As is that M&As generally occur between the same industry within communities. Finally, we calculate the clustering coefficient of directed networks to analyze the clustering properties of the network with the community structures. The clustering coefficient of the network indicates that the number of triangular configuration is very few, which illustrates that the relationship of a company’s neighbors is weak. This work provides insight to structural properties of directed networks based on the M&As from the perspective of complex systems. © 2019 Elsevier B.V. All rights reserved.
∗ Corresponding author. E-mail address: [email protected] (Q. Guo). https://doi.org/10.1016/j.physa.2019.04.133 0378-4371/© 2019 Elsevier B.V. All rights reserved.
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1. Introduction Mergers and acquisitions (M&As) [1–5] are among the most important investment decisions made by a company, given their strategic nature and the long-term impact such decisions have on the operational and financial restructuring of the company. Existing literature has evolved extensively over the last few decades with the result that a number of theories on M&As have been proposed and empirically tested. Hoberg and Phillips [6] pinpointed product market synergy as important drivers of M&As, and contributes to a broader literature on asset complementarity and mergers [7]. Fan and Goyal [8] demonstrated the importance of vertical relatedness of firms’ industries for merger outcomes. Ahern and Harford [9] argued that both intra- and interindustry merger waves are driven by customer–supplier relations between industries. In recent years, researchers have begun to focus their interests on corporate control activity in emerging markets, in particular China. Chinese listed firms have gained the world’s attention with several ambitious, high-profile crossborder mergers and acquisitions. Chen et al. [10] found that investors are indeed skeptical of cross-border mergers and acquisitions deals when the government is the majority owner (i.e., principal–principal conflicts) by investigating a sample of cross-border mergers and acquisitions involving Chinese firms from 2000 to 2008. Bhabra et al. [11] examined 136 M&A deals from 1997 to 2007 initiated by Chinese companies listed on the Shanghai and Shenzhen Stock Exchanges. They showed that the Chinese M&A market is dominated by domestic deals with unlisted targets that are either standalone private firms or wholly owned subsidiaries. Cross-sectional tests showed that announcement period returns are related to the acquirer’s ownership status, industry relatedness of the acquirer and target, capital structure changes of the acquirer and the nature of the unlisted target. And they found no change in operating performance from the pre to the post acquisition period for the acquirers. Complex networks have been widely used in science and technology because of their ability to represent several systems [12–15]. Within the framework of a complex network perspective, an increasing body of literature has been studying M&As. Havila et al. [16] investigated the spread of change in business networks with focus on critical events as triggers of radical change. They found that M&As may cause changes that spread in the business networks, and M&As are investigated as triggers of radical network change in particular. Öberg et al. [17] used the concepts of ‘network pictures’ [18] and ‘networking’ to illustrate and analyze changes in managerial sense-making and networking activities following a merger or acquisition. They showed that following a merger or acquisition managers may need to adapt their previous network pictures in a radical way; these adaptations are, however, not always realized as shifts in ¨ network pictures and adjustments in networking activities by all the managers involved. Duenas et al. [19] analyzed the world web of M&As using a complex network approach. In contrast to the international trade network (ITN), they found that international M&A network was characterized by a persistent giant component with many external nodes and low reciprocity. Clustering patterns were very heterogeneous and dynamic. Many networks exhibit the property of containing community structure [20,21], which has attracted much attention in the past several decades [22–25]. However, they did not analyze the community structures of company’s merger and acquisition networks and network structure characteristics of listed companies for M&As from the perspective of macroscopic level. Inspired by above ideas, we detect community structures of M&A network (MAN) and analyze the properties of mergers and acquisitions for Chinese listed companies in this paper. Firstly, we construct temporal directed networks by preprocessing the data set with Chinese listed companies’ M&A events from 2000 to 2017, where the nodes are the companies, the links represent flows for the M&As, and analyze the evolution properties of the M&A data. Then, we detect the community structure [26–29] of the largest connected component for MAN using Infomap algorithm to investigate the structural properties of MAN. Then, we calculate the modularity of directed networks to evaluate the performance of the community structures. The result shows that the network has clear community structures with the modularity Q = 0.8757. Furthermore, we introduce a parameter η to investigate the industry characteristics for each community. The empirical results indicate that there are a large percentage of companies belonging to the same industry for each community we list. Finally, we further analyze the clustering of the network with community structures, and find that the number of triangle configuration is few, which illustrates that the relationship of a company’s neighbors is weak by calculating the clustering coefficient of the largest connected component. 2. Model and methods In this section, we introduce the model and methods used in this paper. Based on the network science, we investigate the Chinese listed company mergers and acquisitions. The Chinese company M&A network is constructed, which is introduced in the following. 2.1. The construction of network Using the data collected by this paper, we can define the directed M&A network (MAN) in its binary representation. The network at a given point of time t is represented by a directed network, where the nodes are the companies linked by M&A flows, the number is N(t) and links are fully characterized by the N(t) × N(t) asymmetric matrix A(t), with
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entries aij (t) =1 if M&As flows from company i to company j are strictly positive, i.e. a flow of M&As from company i to company j. In order to investigate the characteristics of all the M&A events we collected, we integrated the networks at all times and merged them into a whole network G = (V , E), where V , E are the sets of nodes and links of the network respectively, denotes as MAN. Finally, we extract the largest connected component (LCC) to illustrate the structural properties for M&As. In a network, the mean path length is the average shortest path between two nodes. In this paper, we consider the network as an undirected network when calculating the shortest path. Let dij be the length of the shortest path between nodes i and j. The mean path length is the average of the shortest path length, averaged over all pairs of nodes. For an undirected network of n nodes, the mean path length L is L=
1
∑
n(n − 1)
dij ,
(1)
i̸ =j
where the sum is over all pairs of distinct nodes. The diameter D of the network is the maximum of the shortest path length between two nodes. If two nodes are disconnected, meaning there is no path between them, then the path length between them is infinite. As a consequence, if a network contains disconnected components (collections of nodes that have no paths between them), then the mean path length L also diverges to infinity. One possibility to avoid the divergence is to limit the summation in formula (2) only to couples of nodes belonging to the largest connected component [30]. An alternative approach, that is useful in many cases, is to consider the harmonic mean [31] of geodesic lengths, and to define the so-called efficiency ℓ of G as ∑ 1 1 ℓ= , (2) n(n − 1) dij i̸ =j
The density Den of a network containing n nodes is defined as the ratio of the number of links m actually present in the network to the maximum possible number of links. m Den = , (3) n(n − 1) Network clustering is a well-known concept in complex networks, clustering coefficient can be measured by the percentage of pairs of i’s neighbors that are themselves neighbors, i.e. by the ratio between the number of triangles in the network G with i as one node and the number of all possible triangles that i could have formed. In directed networks, links are oriented and neighboring relations are not necessarily symmetric. The clustering coefficient for node i (CCi ) in directed networks [32] can be thus defined as the ratio between all directed triangles actually formed by i (labeled as tDi ) and the number of all possible triangles that i could form (labeled as TDi ). CCi =
tDi TDi
.
(4)
Degree correlation [33] describes the relationship between the degrees of nodes that link to each other and could reveal the network topology which belongs to assortative network, disassortative network or neutral network. Since nodes in directed networks have both an in-degree and an out-degree, we introduce a set of four directed assortativity measures. β Let α, β ∈ {in, out } index the degree type, and dαl and kl be the α− and β−degree of the source node and target node for link l. Then, the set of assortativity measures using Pearson correlation is defined as follows, r(α,β ) =
m−1
∑
l
β
[(dαl − dα )(kl − kβ )] , σ ασ β
(5)
√
where m is the number of links in the network, dα = m−1 l dαl , and σ α = m−1 l (dαl − dα )2 , and kβ and σ β are similarly defined. In each correlation the links point from the node with the α−indexed degree to the node with the β−indexed degree. Classes of directed networks show common patterns across the four directed assortativity measures: r(in,out) , r(in,in) , r(out ,in) , r(out ,out) . The first element in the parentheses labels the degree of the source node of the directed link, and the second labels the degree of the target node. Thus r(in,out) quantifies the tendency of nodes with high in-degree to connect to nodes with high out-degree, and so on.
∑
∑
2.2. The community structure detection In order to investigate the structural patterns of Chinese listed company mergers and acquisitions, we have detected the community structure of the largest connected component of the M&A network. The method we use in this paper is the classic community structure detection algorithm (Infomap algorithm) on the directed network. Rosvall and Bergstrom [34] proposed a method (called Infomap) to identify communities in directed networks, by combining random walks and compression principles. That is, the modules of the network can be recognized based on how fast information flows on them. The authors apply the concept of random walks to describe the process of information
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X.-Y. Guo, K. Yang, X.-M. Wu et al. / Physica A 526 (2019) 120897 Table 1 The evolution properties of the M&A data. Ncom is the number of companies related to M&As, Nma represents the number of M&A events. Nc denotes the number of connected components for the data sets. Ncom Nma Targets(No.) Acquires(No.) Nc
2000
2005
2010
2015
2017
294 182 141 153 112
2022 1330 1004 1018 714
2112 1366 1004 1151 772
2786 1872 1069 1717 932
3673 2325 1554 2129 1362
flow in the network and the clusters can be extracted by compressing the description of the random walk. A community corresponds to a group of nodes in which the random surfer is more likely to be trapped in, visiting more time nodes of the group than other nodes outside of that. Thus, intuitively, a community would correspond to a group of nodes in which the random walk can be compressed better and the problem can be reformulated as a coding one: the goal is to select a partition M of the n nodes into c communities, minimizing the description length of the random walk. At the first step, each node in the network is described by a unique codeword based on the visiting frequency of the random walk. Using Huffman coding, shorter codewords are assigned to more frequently visited nodes. At the second step, the random walk trajectory on the network can be described following a two-level description: unique names (codewords) are assigned to the clusters of the network (coarse-grained structure), while the codewords for the description of nodes inside a module are reused (fine-grained structure). Thus, reporting only the codewords that have been assigned to communities, a coarse grained description of the network is achieved. The procedure is similar to the one used while designing a geographic map; unique names are assigned to cities (communities in our case), while names for the streets (nodes in our case) of a city can be reused. Then, the clustering problem can be expressed as finding the partition that yields the minimum description code length. If the network has a well-defined community structure, the above twolevel description scheme will produce shorter code length: the random walk will jump between different communities infrequently and thus the description length will be shorter (since the codewords represent individual nodes are shorter). The minimization of the description length can be achieved combining greedy search and simulated annealing methods. Furthermore, we use the modularity function Q [35] as the standard to evaluate the performance of Infomap algorithm. The function can be defined as follows: Q =
1 ∑ m
[Aij −
ij
out kin i kj
m
]δci ,cj .
(6)
where δci ,cj = 1 if the community assignments ci and cj of nodes i and j are the same and 0 otherwise. 3. The experimental analysis 3.1. Data set In this paper, the data we used for the analysis is extracted from Choice financial terminal. It is a financial big data platform owned by Orient Wealth, which covers information on market data of multiple investment types, has a convenient data browser and thematic design, and assists investors in data extraction, analysis and all-round research. We collect the data set which is the Chinese listed company’s M&A events covering the period from 2000 to 2017. The recorded transactions (in volume) referring to M&A activity include the name of the listed companies, the properties of companies, the industries that the companies belong to, the time when the transaction was closed, and the purchase amount of money for M&As and other information. We preprocess the data set, remove the invalid records and the data that do not meet the conditions. 3.2. Statistical properties of the M&A data Firstly, we extract the basic information of the data set we collected. The evolution properties of the M&As for Chinese listed companies in different years are shown in Table 1. We distinguish between acquirers, companies merge or acquire other companies, and targets, companies merged and acquired by other companies. Table 1 shows the number of the listed companies which related to M&As and the number of M&A events from 2000 to 2017. The number of acquirers/targets making up a high percentage (50%) to/from targets/acquires is very concentrated, although it slightly increases over time, which may indicate a spread of acquirers to new markets. As can be seen from the table, the number of companies that related to the M&As and the Chinese listed company M&As has growth trend. The number of the connected components, as a proportion of the number of companies in the network in a given year, reaches up to 37%, which indicates M&A relations are generally unilateral. Then, we analyze the properties and industries of the companies for the listed company M&As in each year. As there are many companies which are not given the properties of the company in the data set, we only analyze the M&A events in
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Fig. 1. The number of companies for different properties and industries in mergers and acquisitions from 2000 to 2017. We can find that the number of state-owned enterprises is larger than the others before 2014, however, the number of private enterprises has occupied the first place, exceeding the number of state-owned enterprises after 2014. Meanwhile, the proportion of the real estate industry has decline trend, and the proportion of industrial machinery and group companies has increased from 2014.
which the companies are given the properties of the company. The results are shown in Fig. 1. As can be seen from Fig. 1(a), the state-owned enterprises and private enterprises account for a relatively large proportion of the listed company M&A events in each year. In particular, the number of state-owned enterprises was larger than that of private enterprises from 2000 to 2013, however, the number of private enterprises has surpassed that of state-owned enterprises from 2014. As there are many industry categories of companies in the data set, and the number of companies in many industries is few, we investigate the evolutions of the industries which listed the top five company industries in 2017. Similarly, we only analyze the companies which labeled the industries in the data set. The result is shown in Fig. 1(b). We can find that the number of companies belonging to real estate industry has been relatively large before 2013, which indicates the real estate industry is active in the market. However, the proportion of the number of companies in industrial machinery and group companies, chemicals and pharmaceuticals, electronic equipment and other industries surpassed the real estate industry after 2014, indicating that the real estate industry gradually has been stable in the market, while other industry companies have been adjusted. Finally, we build the temporal directed M&A networks at each time based on the data set. In order to further analyze properties of M&As from a global perspective, we have integrated the networks from 2000 to 2017 to a whole network, denote as MAN. There are 21,885 nodes, and the number of connected components is 3669, which shows that most of nodes are disconnected with each other in the MAN. The density of the MAN is 4.04 × 10−5 , which indicates the MAN is a low density network. In addition, we also calculate the network’s efficiency ℓ, which is 0.01147, as the network is disconnected. This illustrates that the possibility of reaching nodes with each other in the network is small, which means that the network is sparse. Furthermore, the number of nodes of which out-degree is 1 accounts for 70.3%, and the percentage of the number nodes of which in-degree is equal to 1 is 82.6%, which indicates that a company generally acquires one company, and a company is generally only acquired by one company. 3.3. The community structures of the MAN In order to investigate the structural properties of the integrated network, we extract the largest connected component from MAN and further analyze the network structural patterns for the M&As. Firstly, we investigate the basic structural properties of the largest connected component, analyze the basic structural properties of largest connected component. The results show that the number of nodes and links of the largest connected component are 8030, 8836 respectively, and the density of the largest connected component is 1.37×10−4 , which indicates the largest connected component is a low density network. The average shortest path length L of the largest connected component is 13.487 and the diameter D is 45, which illustrates that the average path length where the nodes in the network reach with each other is very long and the nodes have a weak connected relationship with each other. Then, we analyze the macroscopic structural properties by identifying the community structures of directed connected component using the Infomap algorithm and the result shows that the directed connected component is divided into 17 communities. We calculate the modularity Q of the directed network after detecting the community structure to measure the accuracy of the community structure. The modularity Q = 0.8757 indicates that the Infomap algorithm well detect the community structure in the directed M&A network, and the M&A network also has clear community structure. We further investigate the company industries within the community to analyze the characteristics of community structure. We calculate the proportion of companies belonging to the same industry in top seven size communities (The number of nodes in top seven communities accounts for 72.7% of total nodes in the all communities). The proportion of the top three industries of companies in each community is given as shown in Table 2. The ratio η describes the proportion of the number of companies labeled the same industry to the total number of companies within
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X.-Y. Guo, K. Yang, X.-M. Wu et al. / Physica A 526 (2019) 120897 Table 2 The proportion of the company’s industry in the top seven communities. The ratio η is the proportion of the number of companies which belong to a same industry to the total number of companies in the community. Label
The industries
η (%)
1
Architecture and engineering Real estate development Industrial group enterprise
8.25 5.71 4.02
2
Electric utility Pharmaceutical Industrial group enterprise
12.35 5.98 5.98
3
Aerospace and Defense Real estate development Asset Management and Escrow Bank
7.51 5.78 5.20
4
Electric utility Real estate development Sea transportation
8.45 7.75 7.04
5
Real estate development Steel Trading company and distributor
8.18 6.92 5.66
6
Investment banking and brokerage Industrial group enterprise Real estate development
8.61 6.62 5.96
7
Real estate development Coal and consumer fuel Building materials
8.11 6.76 5.41
a community. As there are many industry categories in each community, the average number of industry categories for the top seven size community is 60, and there are even 103 industry categories in the largest size community, thus the proportion of industries for each community is relatively small. From Table 2, one can find that the first-ranked industries in each community are different, except for the fifth and seventh communities. It indicates that most of the companies in a community belong to the same industry. In details, the number of companies belonging to architecture and engineering accounts for 8.25% in the largest size community. It illustrates that the industry labeled the companies in the community mainly relate to the architecture and engineering. For other communities, the same conclusion can be drawn. These results show that the listed company M&As generally occur between the same industry. In addition, we also find that the real estate industry has a large proportion in each community, which indicates that the real estate industry is closely related to other industries. To investigate the clustering of the network with community structure, we calculate the clustering coefficients of the directed network. For directed networks, there are four different patterns of directed triangles that result in four different clustering coefficients in Fig. 2(a). We can see that overall these four clustering coefficients are small and close to zero, which exhibits that the number of triangle configuration in the network is very few. To some extent these kinds of triangles describe the partnership of an company’s neighbors. We find that it is difficult for a company to have a merger relationship with two other companies with mergers and acquisitions. This also determines the special network structure configuration of the company M&A network. We also calculate the four kinds of degree correlation coefficients which quantify the assortative or disassortative tendency of the network shown in Fig. 2(b). The values of r(in,out) correlation coefficient and r(in,in) correlation coefficient are close to zero, which reveals no significant correlation between the in-degree for the source nodes and out-degree or in-degree for the target nodes. However, the r(out ,out) correlation coefficient is −0.1510 and r(out ,in) correlation coefficient is -0.1562. They both show significant negative correlation, which indicates that the companies which have plenty of M&A behaviors tend to merge the companies that have not acquired other companies or not been acquired by other companies. 4. Conclusion and discussions In this paper, we empirically investigate the community structure for Chinese listed company M&As from the viewpoint of network science. Firstly, for the case study for listed company M&A behaviors, it is hard to know the evolution of each industry and the properties of companies of M&As behaviors, which handles the risk and importance analyses from the company M&A complex system. Secondly, the listed company M&As behavior is dynamic and directed, which could bring insight for the theoretical development of network science. We detected the community structure of the largest connected component for MAN using the Infomap algorithm to investigate the structural properties of the M&As. The results showed that the network has clear community structure with modularity Q = 0.8757. By the analysis of the company industries in each community, we found that the M&As generally occurred between the same industry for each community. Finally, the clustering coefficient of the directed network with community structures was calculated. The empirical results indicated
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Fig. 2. The four clustering coefficients with eight different directed triangles and the four degree–degree correlations in directed M&A network. From which, we can find that overall these four clustering coefficients are much small, and the absolute value of the coefficient r(out ,out) and r(out ,in) are relatively large.
that the number of triangular configuration in the network is few, which illustrates that the relationship of a company’s neighbors is weak. We investigated the community structure of M&As with complex networks, the following points should be addressed in the future work. Although we have presented various characteristics of the M&A network and drawn some conclusions, we did not analyze the relationship between the performance of M&As and the network structure, and not analyze the changes of organizational structure, customer relationship, management and other aspects of the companies before and after the M&A. Secondly, a lot of companies’ information in the original data is not given, such as the properties of the company or the industries, so we will inevitably have deviations for the statistical analysis of the data set. In addition, the empirical analysis in this paper consists mostly of domestic deals. As cross-border deals grow and public targets come into play, future research should examine the whole patterns of acquisition activity in this rapidly transforming market. Overall, our analysis attempted to provide a network characterization of the MAN that can contribute to future research on international networks. Acknowledgments This work is partially supported by the National Natural Science Foundation of China (Grant No. 61773248, 71771152), and the National Social Science Foundation of China (18ZDA088). References [1] J. Bena, K. Li, Corporate innovations and mergers and acquisitions, J. Finance 69 (5) (2014) 1923–1960. [2] P. Deng, M. Yang, Cross-border mergers and acquisitions by emerging market firms: A comparative investigation, Int. Bus. Rev. 24 (1) (2015) 157–172. [3] S. Rossi, P.F. Volpin, Cross-country determinants of mergers and acquisitions, J. Financ. Econ. 74 (2) (2004) 277–304. [4] I.R.P. Cuypers, Y. Cuypers, X. Martin, When the target may know better: Effects of experience and information asymmetries on value from mergers and acquisitions, Strateg. Manage. J. 38 (3) (2017) 609–625. [5] I. Erel, R.C. Liao, M.S. Weisbach, Determinants of cross-border mergers and acquisitions, J. Finance 67 (3) (2012) 1045–1082. [6] G. Hoberg, G. Phillips, Product market synergies and competition in mergers and acquisitions: A text-based analysis, Rev. Financ. Stud. 23 (10) (2010) 3773–3811. [7] M. Rhodes-Kropf, D.T. Robinson, The market for mergers and the boundaries of the firm, J. Finance 63 (3) (2008) 1169–1211. [8] J.P.H. Fan, V.K. Goyal, On the patterns and wealth effects of vertical mergers, J. Bus. 79 (2) (2006) 877–902. [9] K.R. Ahern, J. Harford, The importance of industry links in merger waves, J. Finance 69 (2) (2014) 527–576. [10] Y.Y. Chen, M.N. Young, Cross-border mergers and acquisitions by Chinese listed companies: A principal–principal perspective, Asia Pac. J. Manag. 27 (3) (2010) 523–539.
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