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...des outside the subset. Several definitions of community and methods to detect communities have been proposed in the literature [see 2, for a review]. Most algorithms can be distinguished in divisive =-=[29]-=-, agglomerative [30] and optimization-based [31]. In the latter case, the goodness of the partitions is commonly assessed in terms of the so-called “modularity” [29], defined as follows: Q = 1 2l ∑ i,...

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...ng the method of [24] that belongs to the optimization class and is one of the few algorithms suitable for the investigation of large networks with no imposed constraints on the number of communities =-=[25]-=-. In order to asses the robustness of the resulting community partitions, we have compared the community structure in the empirical network with the one obtained from a random link formation process, ...

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...duction A recent work has studied the global structure of ownership network with respect to the issue of the corporate control [1]. In this paper, instead, we carry out an in-depth community analysis =-=[2]-=- of the same network, in order to address questions concerning the level of geographical integration and the role of the financial sector in the global economy. An economic network is a structure in w...

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...nnected, with the large majority of the nodes belonging to a large connected component, which is itself organized in several communities. The community analysis is performed by applying the method of =-=[24]-=- that belongs to the optimization class and is one of the few algorithms suitable for the investigation of large networks with no imposed constraints on the number of communities [25]. In order to ass...

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...ommunity and methods to detect communities have been proposed in the literature [see 2, for a review]. Most algorithms can be distinguished in divisive [29], agglomerative [30] and optimization-based =-=[31]-=-. In the latter case, the goodness of the partitions is commonly assessed in terms of the so-called “modularity” [29], defined as follows: Q = 1 2l ∑ i,j∈C [ai,j − kikj 2l ], (1) where l is the total ...

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...d the community structure in the empirical network with the one obtained from a random link formation process, accounting for the constraints on the degree distribution and on the ownership structure =-=[26, 27, 18]-=-. The comparison reveals that for the rewired networks the community structure is quite homogeneous across realizations and it differs considerably from the one of the empirical network, meaning that ...

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...et. Several definitions of community and methods to detect communities have been proposed in the literature [see 2, for a review]. Most algorithms can be distinguished in divisive [29], agglomerative =-=[30]-=- and optimization-based [31]. In the latter case, the goodness of the partitions is commonly assessed in terms of the so-called “modularity” [29], defined as follows: Q = 1 2l ∑ i,j∈C [ai,j − kikj 2l ...

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...[5, 6], financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates =-=[14, 15, 16]-=-, and those on firm ownership [17, 1, 18, 19, 20]. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresp...

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... and the Role of Financial Sector One can also think of communities as the nodes of a network, where the links connecting them are weighted by the number of links between firms in the two communities =-=[29]-=- [31]. The network of the top eight communities by size is shown in Fig. 5. In order to gain further insight into the whole community network, we start with a basic network analysis. The bow-tie decom...

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...1, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership =-=[17, 1, 18, 19, 20]-=-. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresponding Author †SB acknowledges support from FET O...

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...etworks. 2Asian firms are dominant only in few communities. The existence of only few and small Asian communities could be due to the traditional organization of Asian corporations in business groups =-=[32]-=-, where members are densely connected in relatively small groups with few or no connections with external firms. 7/19 Stefania Vitali, Stefano Battiston: The Community Structure of the Global Corporat...

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... on the number of communities [26]. We first perform the community analysis by applying the method of [27] (hereafter, Louvain method) and we further apply the method of the hierarchical map equation =-=[28]-=- (hereafter, Infomap method). In order to asses the robustness of the resulting community partitions, we compare the community structure in the empirical network with the one obtained from a random li...

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...entities by means of one or more specific types of relationships. Previous empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade =-=[3, 4]-=-, international financial exposures [5, 6], financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boar...

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...and, within each level, to further split modules apart. While this may be an interesting question, it is not the focus of our paper. Here, we are interested in communities meant as groups of interest =-=[40]-=-. Therefore, in line with previous community analyses in ownership networks [23], when running the community detection algorithms we consider the network as undirected. Further, we want to compare the...

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...vious empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures [5, 6], financial networks =-=[7, 8, 9, 10, 11, 12, 13]-=- More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership [17, 1, 18...

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...tive values. Therefore, the values obtained have to be compared with those obtained in ensembles of rewired networks (see more below). Despite the resolution limits of modularity optimization methods =-=[36]-=-, especially in detecting small clusters, it has been found to be one of the best methods for network partition. Among the available detection algorithms of the optimization-based class, in this study...

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...vious empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures [5, 6], financial networks =-=[7, 8, 9, 10, 11, 12, 13]-=- More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership [17, 1, 18...

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...entities by means of one or more specific types of relationships. Previous empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade =-=[3, 4]-=-, international financial exposures [5, 6], financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boar...

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...larly true for small communities. doi:10.1371/journal.pone.0104655.g003 Communities in the Corporate Network PLOS ONE | www.plosone.org 6 August 2014 | Volume 9 | Issue 8 | e104655 Mutual Information =-=[43]-=- and the Variation of Information [44] methods. The first one is a measure of the coincidence of two partitions, ranging from 0 -minimum coincidence- to 1 -maximum coincidence-. In our networks, the c...

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...[5, 6], financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates =-=[14, 15, 16]-=-, and those on firm ownership [17, 1, 18, 19, 20]. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresp...

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... we apply the Louvain method which is one of the few methods that are suitable: (i) to analyze large networks with good scalability properties [37] and (ii) to avoid ex-ante assumptions on their size =-=[26,38]-=-. For the sake of robustness, we also run the community analysis with the Infomap algorithm proposed by [28]. Indeed, among the many available ones, this methods has been proved to be one of the best ...

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...vious empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures [5, 6], financial networks =-=[7, 8, 9, 10, 11, 12, 13]-=- More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership [17, 1, 18...

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...types of relationships. Previous empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures =-=[5, 6]-=-, financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 1...

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...vious empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures [5, 6], financial networks =-=[7, 8, 9, 10, 11, 12, 13]-=- More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership [17, 1, 18...

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...; Firm Localization; Financial Sector JEL codes: F64; L14; G2; G3 1 Introduction A recent work has studied the global structure of ownership network with respect to the issue of the corporate control =-=[1]-=-. In this paper, instead, we carry out an in-depth community analysis [2] of the same network, in order to address questions concerning the level of geographical integration and the role of the financ...

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... hereafter, which is based on a flow and information theoretic clustering method, maintain the geographical and sector properties. Finally, we consider communities as themselves forming a metanetwork =-=[31]-=-, in which the link between any two given communities reflects the number of ownership relations among firms from the two communities. We assess the importance of each community in the network by usin...

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...vious empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures [5, 6], financial networks =-=[7, 8, 9, 10, 11, 12, 13]-=- More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership [17, 1, 18...

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...in the literature are suitable to the investigation of large networks without imposing constraints on the number of communities [26]. We first perform the community analysis by applying the method of =-=[27]-=- (hereafter, Louvain method) and we further apply the method of the hierarchical map equation [28] (hereafter, Infomap method). In order to asses the robustness of the resulting community partitions, ...

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...t. Several definitions of community and methods to detect communities have been proposed in the literature (see [2] for a review). Most algorithms can be distinguished in divisive [33], agglomerative =-=[34]-=- and optimization-based [35]. In the latter case, the goodness of the partitions is commonly assessed in terms of the so-called ‘‘modularity’’ [33]. The modularity takes values between {1 and 1 and co...

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...vious empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures [5, 6], financial networks =-=[7, 8, 9, 10, 11, 12, 13]-=- More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership [17, 1, 18...

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...of the Global Corporate Network community structure of two small networks, the Italian board and ownership networks, the other community analyses have focused on correlation networks in stock markets =-=[22]-=- and in foreign exchange markets [23]. The study of the transnational corporation (TNC) ownership network reveals that corporations are well connected, with the large majority of the nodes belonging t...

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... to some other actors by means of relationships of several types. Previous empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade =-=[3,4]-=-, international financial exposures [5,6] and financial networks [7–13]. More in detail, previous works on networks relevant to corporate governance include: (i) those on corporate boards, e.g., inter...

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...d the community structure in the empirical network with the one obtained from a random link formation process, accounting for the constraints on the degree distribution and on the ownership structure =-=[26, 27, 18]-=-. The comparison reveals that for the rewired networks the community structure is quite homogeneous across realizations and it differs considerably from the one of the empirical network, meaning that ...

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...10.1371/journal.pone.0104655.g003 Communities in the Corporate Network PLOS ONE | www.plosone.org 6 August 2014 | Volume 9 | Issue 8 | e104655 Mutual Information [43] and the Variation of Information =-=[44]-=- methods. The first one is a measure of the coincidence of two partitions, ranging from 0 -minimum coincidence- to 1 -maximum coincidence-. In our networks, the comparison of the two partitions yields...

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...[5, 6], financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates =-=[14, 15, 16]-=-, and those on firm ownership [17, 1, 18, 19, 20]. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresp...

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...nity structure of two small networks, the Italian board and ownership networks, the other community analyses have focused on correlation networks in stock markets [22] and in foreign exchange markets =-=[23]-=-. The study of the transnational corporation (TNC) ownership network reveals that corporations are well connected, with the large majority of the nodes belonging to a large connected component, which ...

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... that no competing interests exist. * Email: stefano.battiston@.uzh Introduction A recent work has studied the global structure of ownership network with respect to the issue of the corporate control =-=[1]-=-. In this paper, instead, we carry out an in-depth community analysis [2] of the same network, in order to address questions concerning the level of geographical integration and the role of the financ...

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...re in the business activity industry (39%), while the services and manufacturing sectors account for 20% and 18% respectively. Further, we apply the community characterization algorithm introduced in =-=[33]-=-. This statistical method reveals if a particular attribute of a community is “over-expressed”, i.e., if its frequency in the community is larger than what expected from a random occurrence of the att...

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...e two communities. We assess the importance of each community in the network by using DebtRank, a centrality measure recently introduced in the complex networks literature in the context of economics =-=[9]-=-. In particular, we apply this method to verify whether the financial sector is a major source of connection among different communities. We find that the community centrality and, thus the potential ...

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...types of relationships. Previous empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3, 4], international financial exposures =-=[5, 6]-=-, financial networks [7, 8, 9, 10, 11, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 1...

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...1, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership =-=[17, 1, 18, 19, 20]-=-. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresponding Author †SB acknowledges support from FET O...

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...terlocking directorates [14–16], and those on firm ownership [1,17–20]. In general, little attention has been devoted to the community structure of economic networks, with the remarkable exception of =-=[21,22]-=-. Apart from the study of [23] on the Italian corporate board and ownership networks, the other community analyses have focused so far on correlation networks in stock markets [24] and in foreign exch...

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...e the community structure in the empirical network with the one obtained from a random link formation process, accounting for the constraints on the degree distribution and on the ownership structure =-=[18,29,30]-=-. The comparison reveals that for the rewired networks the community structure is quite homogeneous across realizations and differs considerably from the one of the empirical network. This means that ...

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...rations (TNC), defined as those companies that are headquartered in one country and operate in at least one foreign country, by owning partially, at least 10% of the shares, or wholly other companies =-=[28]-=-. We obtain a list of 43060 TNCs, located in 115 different countries. The major part of these TNCs have their headquarters in Europe and the US. Nevertheless, some of them are also located in off-shor...

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...1, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership =-=[17, 1, 18, 19, 20]-=-. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresponding Author †SB acknowledges support from FET O...

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...e the community structure in the empirical network with the one obtained from a random link formation process, accounting for the constraints on the degree distribution and on the ownership structure =-=[18,29,30]-=-. The comparison reveals that for the rewired networks the community structure is quite homogeneous across realizations and differs considerably from the one of the empirical network. This means that ...

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...terlocking directorates [14–16], and those on firm ownership [1,17–20]. In general, little attention has been devoted to the community structure of economic networks, with the remarkable exception of =-=[21,22]-=-. Apart from the study of [23] on the Italian corporate board and ownership networks, the other community analyses have focused so far on correlation networks in stock markets [24] and in foreign exch...

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...rations (TNC), defined as those companies that are headquartered in one country and operate in at least one foreign country, by owning partially, at least 10% of the shares, or wholly other companies =-=[32]-=-. We obtain a list of 43060 TNCs, located in 115 different countries. The major part of these TNCs have their headquarters in Europe and the US. Nevertheless, some of them are also located in off-shor...

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...C. However, with a relative size of 7.74%, the LSCC of the meta-network is still much smaller in relative terms than in other paradigmatic real-world networks, such as wikipedia or the world-wide-web =-=[45]-=-. The degree statistics yields: average in-degree ~2:5+8:7, max indegree ~557, average out-degree ~2:5+62, max out-degree ~4146. For the shortest paths we find: maximum ~4; average 2:43+0:51. The link...

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...1, 12, 13] More in detail, regarding corporate governance, there are two main groups of works: (i) those on corporate boards, e.g., interlocking directorates [14, 15, 16], and those on firm ownership =-=[17, 1, 18, 19, 20]-=-. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of [21], which analyzes the ∗Corresponding Author †SB acknowledges support from FET O...

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...locking directorates [14, 15, 16], and those on firm ownership [17, 1, 18, 19, 20]. However, in these disciplines little attention has been devoted to the community structure. Apart from the study of =-=[21]-=-, which analyzes the ∗Corresponding Author †SB acknowledges support from FET Open Project FOC "Forecasting Financial Crises" nr. 255987. 1/19 ar X iv :1 30 1. 23 63 v1s[ qfin .G N]s1 1 J ans20 13 Stef...

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...and those on firm ownership [1,17–20]. In general, little attention has been devoted to the community structure of economic networks, with the remarkable exception of [21,22]. Apart from the study of =-=[23]-=- on the Italian corporate board and ownership networks, the other community analyses have focused so far on correlation networks in stock markets [24] and in foreign exchange markets [25]. Our study o...

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...nships of several types. Previous empirical studies in socio-economic networks, that are relevant for our work, include those focusing on: international trade [3,4], international financial exposures =-=[5,6]-=- and financial networks [7–13]. More in detail, previous works on networks relevant to corporate governance include: (i) those on corporate boards, e.g., interlocking directorates [14–16], and those o...

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...lgorithms of the optimization-based class, in this study, we apply the Louvain method which is one of the few methods that are suitable: (i) to analyze large networks with good scalability properties =-=[37]-=- and (ii) to avoid ex-ante assumptions on their size [26,38]. For the sake of robustness, we also run the community analysis with the Infomap algorithm proposed by [28]. Indeed, among the many availab...

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...he decision making process in B’s board of directors. The presence of representatives of A in B determines also a flow of information from A to B, so that decisions may spread from a board to another =-=[39]-=-. On the other side, the economic performance of B, especially if it is a subsidiary of A, affects A’s profits via its shares. Further, A may shift resources from a subsidiary to another for strategic...

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...(Asian firms, indeed, are dominant only in few communities. The existence of only few and small Asian communities could be due to the traditional organization of Asian corporations in business groups =-=[41]-=-, where members are densely connected in relatively small groups with few or no connections with external firms.). For the characterization of communities in terms of sectors, we group all sectors in ...