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The main purpose of this exploratory work is to assess the similarities among selected actors’ attributes and specific actors’ centralities, along with the similarities between the attributes of detected subgroups and subgroup centralities. Despite being an exploratory study, two main hypothesis arise and will be tested: Do actors with higher indegree centrality also have higher revenue, production or profit? Do subgroups of actors with higher indegree centrality have also higher revenue, production or profit?
The similarity assessment was only made available through the gathering of relational data from the global automotive alliances between 2011 and 2013, mostly from the Global Automotive Partnerships guide prepared by Automotive News magazine, whose document showed alliances related to 20 major world manufacturers and four governance structures; the guide comprised in 2011 the following automakers: BMW, Chrysler, Daimler, FAW, Fiat, Ford, General Motors, Honda, Hyundai, Mazda, Mitsubishi, Nissan, Porsche, PSA, Renault, SAIC, Subaru, Suzuki, Toyota, Volkswagen. For 2012 and 2013, the guide integrated Porsche to Volkswagen due to the acquisition of the first by the latter in 2012. As for the four governance structures, they were: equity stake ownership (ESO), contract assembly (CA), technical and parts alliance (T&PA) and joint ventures (JV).
Since the data collected were summarized by the magazine, additional relations were added by the author in order to increase the number analyzed. The number of relations sampled to be included in the guide was not available, therefore the authors opted to select at least a suited sample of the relations based primarily on the guide and also on the information found in other specialized automotive sources to complete and verify the absent relations. According to OICA, the 19 manufacturers analyzed in the study correspond to almost 85% of the total automotive global production in 2013. The total number of actors in the networks were 276, 283 and 288 respectively over the years.
Previously the collection of the relational data, the authors decided to treat them as directed, observing the money flow between the two actors for each alliance observed. So for ESO relations, the direction pointed to the owner, CA pointed to the assembly line proprietary, T&PA pointed to the actor who sold the technology and JV pointed to the joint ventures’ owners. The relations’ directions were fundamental to calculate later the actors’ and subgroups’ indegree centrality for the two main hypothesis tested. Concerning the attribute data, they were collected through the OICA database for production, and through the manufacturers’ annual reports of each one for revenue and profit. Groups had their attributes added according to the actors' attributes pertaining to the specific group.
All the relational data were arranged yearly as an edge list in Microsoft Excel with the type of relation in the third column right after the two actors. Then, the data were transferred to UCINET to be transformed into asymmetric matrices. Each year of observation had four different relations, which were integrated into a single network, called a multiplex network. Whereas the network digraphs or sociograms were multiplex, the analyses were not. The four different relations for each year were aggregated into a single-valued asymmetric matrix, where the values were basically added according to the presence of ties between two actors among the four relations. At first, the subgroups were identified using Louvain’s method algorithm for the directed weighted adjacency matrices. After, their respective indegree, outdegree and k-step reach (k=2) normalized and non-normalized centralities were also calculated. Secondly, the indegree and the outdegree normalized and non-normalized centrality measures were calculated with the aforementioned matrices for the actors. Later, the betweenness and the k-step reach (k=2) normalized and non-normalized centralities were calculated for the directed dichotomized adjacency matrices; the normalized and the non-normalized centralities were calculated to make further comparisons within and between the years respectively.
Finally, the Pearson’s product moment correlation coefficient was calculated for each similarity assessed between the actors’ attributes and its normalized centralities, as well as for the added attributes for the resulting groups and its centralities. Regarding the correlations statistical significance, the software SPSS was used instead of the software UCINET. However, the author paid attention to the statistical procedure used in SPSS in order not to violate the assumptions in Social Network Analysis of interdependency between each actor and the unknown probability distribution and the non-random sampling of the data. Thus, the SPSS non-exact permutation test Monte Carlo was used in lieu of the non-exact permutation test in UCINET to facilitate the whole analysis.
<!--[if !supportLists]-->· <!--[endif]-->Moderate to strong correlation for the groups, statistically significant at p < 0.05 for 2011 and p < 0.01 for 2012 and 2013.
For being mainly an exploratory work, much of the observations will be shown in tables and graphs, along with the three multiplex networks and the other three networks demonstrating the subgroups found.
This particular work would help managers to understand the networks in which their organizations are embedded in, notwithstanding which actors to start an alliance with. The approach to social network analysis gives an enormous strategic advantage to the company.
The research seeks to show and analyze among 20 major automakers in the global automotive industry, how the actors are organized concerning the network topology and how central they are, assessed by the indegree centrality regarding their structural position. Furthermore, two hypotheses will be proposed, and analyzes of similarities will be made through correlations tests between the actors’ both production, revenue and profit performance attributes and indegree centrality values. In order to accomplish this, we collected 1359 relationships of four specific governance structures from 2011, 2012 and 2013 mainly from the Automotive News magazine guide, and we arranged them in edge lists observing particularly the money flow for each arc. The algorithm called the Louvain method identified cohesive subgroups, and the indegree centrality algorithm counted the money flow. The results show a network structure characterized by communities, as well as moderate to strong similarities between the actors and the subgroups formed by them with their respective revenue and the money flow for the three years accounted here.
Interorganizational alliance networks or constellations of alliances are denominations assigned to the set or collection of the various relationships that actors or groups of network actors have in their alliance portfolio, for example, joint ventures, joint research and development, joint projects and production, marketing, among others, usually for strategic purposes of mutual benefit and whose competition and cooperation is exercised in specific industry (BAMFORD; GOMES-CASSERES; ROBINSON, 2003; DAS; TENG, 2003; GULATI; WOHLGEZOGEN; ZHELYAZKOV, 2012).
Such networks of alliances are in evidence given various features relating to the modern economy, such as global economic aspects, increasing complexity in the fabrication of goods, the need to reach a global scale and establish technical standards, as well as the relationship between companies in development of new technologies (GOMES-CASSERES, 1994), that motivate organizations to seek to "link markets, combine skills, build momentum, reduce costs and share risks" (BAMFORD; GOMES-CASSERES; ROBINSON, 2003, p. 232).
Social network analysis receives a prominent position in the field of organizational studies (BORGATTI et al., 2009; JACKSON, 2010; KILDUFF; BRASS, 2010) since the existence of underlying social structures to networks of interorganizational alliances have already been explored in several works (GULATI, 1998; GULATI; GARGIULO, 1999; GRANOVETTER, 2005; SHIPILOV et al., 2014). These underlying social structures present patterns of relations or topology formed from the selections oriented to the formation of alliances between actors (DIANI, 2011). These underlying social structures present patterns of relations or topology formed from the selections oriented to the formation of alliances between actors (WANG; NGUYEN; WANG, 2016) or characteristics associated with the relationships themselves (RIVERA; SODERSTROM; UZZI, 2010).
Researches involving network analysis in interorganizational relationships have already shown that companies are more influenced by others that have greater similarity or better structural position, or because they occupy more or less central regions (WANG et al., 2015), because they are members of the same (DAVIS, 2016) or the nature of the alliances managed and shared between them (SHIPILOV et al., 2014).
Specifically, interorganizational alliances in the automotive sector have heterogeneous governance structures as observed between the Renault and Nissan automakers that in the 1990s would become the benchmark for the industry (THE ECONOMIST, 2010). Ford-Mazda also started alliance processes, building networks of shareholder-backed partnerships from the late 1990s (FREYSSENET, 2009) as well as General Motors-PSA and Volkswagen-Suzuki later. Since then, companies such as Toyota have forged alliances with other automakers, either in the creation of a new product (Toyota-Ford and Subaru-Toyota) or the development of new technology (Toyota-BMW) and in the joint operation of a factory with PSA Peugeot Citroën (THE ECONOMIST, 2015). Other examples are the successful alliances between Renault-Nissan-Daimler AG (WANG; NGUYEN; WANG, 2016), Fiat-Chrysler (AUTOMOTIVE NEWS, 2015) and Nissan-Mitsubishi (THE ECONOMIST, 2016).
The plurality of relationships found in alliance networks and mentioned above in the automotive industry is a multiplex network that has a feedback characteristic since the diversity of governance structures reinforces actors to diversify and form new alliances that are different from those already established (LOMI; PATTISON, 2006). Nonetheless, Tatarynowicz, Sytch and Gulati (2016) recently addressed the automotive industry in terms of the technological dynamism influenced by present social structures, including subgroup structures. It was noted that concerning technology alliances, the automotive industry presented itself as a clan network, poorly connected and with strong community structures.
The observed phenomena related to the new characteristics of the modern economy lead to a new structural and relational composition of the groups of companies, leading the organizations belonging to the network to strategically think of the way they will deal with the alliances to be established (GULATI; NOHRIA; ZAHEER, 2000). In addition, the inter-influences of the organizations observed in constellations or networks of alliances raise questions about the interference that the positions occupied by the automakers promote in the network and in particular in the cohesive subgroups of actors, possibly analyzed under the theoretical construct of the clicks (MIZRUCHI; GALASKIEWICZ, 1993, GULATI, GARGIULO, 1999, PROVAN, FISH, SYDOW, 2007).
Particularly in the automotive industry, works such as those performed in Nohria e Garcia-Pont (1991), Garcia-Pont and Nohria (2002), Soda (2011), Sacomano Neto and others (2016), Tatarynowicz, Sytch and Gulati (2016) and Cattani, Porac and Thomas (2017) have already dealt with the identification of subgroups or communities and the relationship between them and the structural aspects that influence the network and the groups, or how the network topology can affect the actors, relations and groups that compose it.
As observed in Wang and others (2015), resources are important for an organization immersed in a network in the acquisition of power and in the control of these resources not only by the dependence coming from the relations themselves, but also by the structural factor observed by the location or position of the actors in the network. However, Gulati, Lavie and Madhavan (2011) present vital factors that influence the performance of a company in a network, and how these companies can take advantage of the network in which they are immersed.
According to Williams (2005), centrality can be used as a structural variable that assists in understanding the dynamics involving power-dependence theory among interrelated actors from the perspective of the interorganizational networks of the concentration of power of more central actors and the addition of dependence of more peripheral actors, such as to be found in Hoffman, Stearns and Shrader (1990).
Also, Provan, Fish and Sydow (2007) present propositions about some characteristics intrinsic to the networks as the centralities of indegree and outdegree. The authors state that these metrics can be an assessment of " the extent to which assets such as resources, information, and clients are coming into an organization from others in the network versus those being sent out to other organizations" (PROVAN; FISH; SYDOW, 2007, p. 484).
The identification of similarities between relational and attribute variables, especially in relationships belonging to the automotive industry, is rare. A work that stands out with the above characteristics is that of Soda (2011) when looking for associations between the patents produced by the actors and relational variables that present the cohesion of actors immersed in the network through the densities of their neighbourhood. However, studies such as Tsai and Ghoshal (1998), Gest, Graham-Bermann and Hartup (2001), Yan and Ding (2009), Croci and Grassi (2014) and several others present analyzes of Pearson and Spearman correlations between measures of performance or attributes of actors and structural measures of centrality in various fields of science and different areas of study..
Social networks analysis can be understood as a set of methods used to understand the social environment by highlighting patterns or regularities in relationships between interacting units (WASSERMAN; FAUST, 1994; SCOTT, 2000). The social environment from the perspective of ARS is constituted, as mentioned, by interactive units called nodes or vertices and the relationships exhibited by them are called loops. This nomenclature comes from the area of mathematics that studies discrete relational structures, called graph theory (KILDUFF; TSAI, 2003; BUTTS, 2008), whose applicability is capillary by several areas of scientific knowledge (BORGATTI et al., 2009). The studies in network analysis analyze four different levels: nodal, dyad, triad and subgroups, where the first and last level here were considered.
Through the analysis of centrality used in social networking works, the actors are studied individually to see which are in more or less central positions, for example, how popular, central/peripheral or even an efficient mediator an actor can to be structured immersed in the network (PRELL, 2012). Hanneman and Riddle (2005) present how each individual actor's understanding can explain the network concerning an actor's power, either by obtaining a more favourable position, having more opportunities and/or fewer restrictions, whereas Kadushin (2012) the metrics of centrality as the popularity of an actor.
According to Scott (2017), the metric degree is the most straightforward algorithm to measure the centrality of an actor in a network and can be used in directional or non-directional, dichotomic or weighted networks. In a very practical way, the degree of a node is given by the number of arcs or links connected to it, since the network is a graph (NEWMAN, 2010). Wasserman and Faust (1994) point out that this metric highlights the activity of an actor in the network, assigning values of 0 for an isolated actor and consequently nothing active, up to n for proportionally more active actors the higher the value of the metric; the authors emphasize that the metric focuses only on the nodes adjacent to the actor. Barabási (2002) points out that in order to understand the different types of networks, analyzing the distribution of links through network nodes, that is, examining the degree of each actor, is a step of paramount importance; the author presents networks of random characteristic and Gaussian distribution of loops, and networks that follow the distribution of the power law, in which very few actors have a high degree value and most nodes have few links.
In directional networks, degree centrality separates into indegree and outdegree; Hansen, Shneiderman and Smith (2011) present that, given a specific node, indegree is the number of bonds that reach the actor and outdegree is the bonds that leave the actor. Several actors in different network contexts interpret indegree metrics in a particular way; Kilduff and Tsai (2003) treat indegree as the popularity of an actor; Wasserman and Faust (1994) address the metrics of indegree as prestige; and Borgatti, Everett and Johnson (2013) contextualize indegree like the prestige or popularity of a node.
One level of analysis, despite the numerous analytical perspectives and paradigms of ARS, is that of subgroups (MARIN; WELLMAN, 2011). Subgraphs of a graph, according to Hansen, Shneiderman and Smith (2011) and Scott (2017), can be understood as a complex combination, of a random nature or not, of a collection of selected points of the whole network, forming smaller groups as well known as clusters or communities. Barabási (2002) and Scott (2017) emphasize that in the studies of the structural properties of social networks the subgraphs are not random in their conception, since the formation of social groups, as well as chemical and biological networks for example, have established characteristics and plausible occurrence of higher identifications.
Doreian, Batagelj and Ferligoj (2005) add that subgraphs are any subsets of nodes and edges contained in the nodes and edges of a primordial graph. Prell (2012, p. 151) defines the term subgroups in networks as "an area of a network larger than a dyad or triad and yet smaller than an entire network"; and Wasserman and Faust (1994), which provide the complementary definition of subgroups in which a high proportion of a subset of the actors share strong, direct, intense, frequent or positive ties, called cohesive subgroups.
The subdivision of a network into subgroups or communities can be measured by the modularity assessment presented by Newman as an attempt to identify substructures, defined by the author as subgroups that have more links within the group than between groups, considering the degree of each node or actor and the size of the group (HANNEMAN; RIDDLE, 2011). As Newman points out (2006, 2010) and proposed in Girvan and Newman (2002), modularity not only considers the low number of lines between substructures or subgroups, but it is also a definition and metric that indicates if there is between groups number of vertices greater or less than would be expected at random, since it "measures the difference between the total fraction of incident lines between groups versus the fraction that would be expected if the lines were placed randomly" (PORTER; ONNELA; MUCHA, 2009, p.9).
The aggregator algorithm of Blondel et al. (2008), christened Louvain's algorithm or Louvain's method by the geographical origin of the algorithm, addresses the modularity criterion (ORMAN; LABATUT; CHERIFI, 2012) and is usually chosen to maximize this modularity and deal with value matrices according to Blondel et al. (2008) and Okraku et al. (2017) as well as non-symmetric matrices according to UCINET software 6,648. The Louvain method consists of two phases, called Vertex Mover Procedure and Coarsening Phase, which are repeated alternately and incessantly until maximum local modularity is obtained (AYNAUD et al., 2011; GACH; HAO, 2013).
According to the authors, the algorithm starts assigning values from 0 to N-1 randomly for each node-community of the network composed of N nodes. In the first phase, the algorithm seeks to find a local optimization through the movement and allocation of the first node (node 0) selected by the algorithm or the researcher, to the community of one of the neighbors of this vertex provided that in this movement the new modularity of the calculated network subsequent to the allocation causes in the greatest possible positive increase of this modularity; this calculation is performed for all neighbors of the selected vertex (node 0). If the increment is negative, then the node returns to its original community.
The above process is applied iteratively until no node is moved and the first phase is terminated. As far as the second phase is concerned, it consists of the fusion of the vertices employing the construction of meta-graphs composed by the communities found at the end of the first phase. At the beginning of the second phase, a graph or partition is created whose vertices are the forming nodes of the found communities. Then the weights of the edges between two of the new nodes of the new graph are given by the sum of the weights of the edges that existed between the vertices of these two communities. The edges that existed between the vertices of the same community create loops or cycles "(AYNAUD et al., 2011, p. 323) in the community of the new graph. In this iterative way, the two so-called pass phases construct a network until maximum modularity is reached and there are no more vertex movements and the algorithm ceases (BLONDEL et al., 2008).
Analogous to the calculation for nodes due to the links that affect them, the centrality of the actors has been extended to metrics that transpose them into subgroups in a graph, as observed in Everett and Borgatti (1999) and Bell (2014). This relationship observed by researchers between centrality and the cohesive structure of subgroups was analyzed in the literature in Bodin and Crona (2009) for example, or in Moody and White (2003) between node connectivity and related social cohesion and immersion.
As presented in Borgatti, Everett and Freeman (2002), the calculation of centralities for groups must be performed when the researcher already has the groups that make up the network under analysis. UCINET 6 calculates the degree centrality for a group of actors based on the number of actors external to the group and who are directly connected to the group members (BORGATTI; EVERETT; FREEMAN, 2002).
Actors with greater indegree tend to have greater attributes of production, revenue or profit.
As noted, we intend here to assess the similarity between more central actors concerning their indegree, and the performance attributes cited above.
The subgroups identified in the network with greater indegree tend to have greater attributes of production, revenue or profit.
Likewise, we intend here to assess the similarity between more central subgroups concerning their indegree, and their production, revenue and profit performance attributes.
According to the research proposal, a longitudinal data collection (WASSERMAN; FAUST, 1994) was performed, observing alliances of worldwide automotive organizations regarding cross-shareholding, joint ventures, manufacturing contracts and alliances of technology and parts, whose analysis data for the period 2011 to 2013 were taken from the database of Automotive News.
The database provided between the years 2005 to 2013 an annual global summary named Guide to Global Automotive Partnerships containing several alliances of the sector of companies selected by the magazine on the date established by the publication, as well as provided guides of the plants of the automakers in North America in 2012 and 2013 and in Europe in 2012, containing which cars of which automakers were mounted on the premises. Regarding the actor attribute data, revenue and profit were collected using the annual reports available to the companies and then the dollar conversions were made according to the exchange rate on the last day of the date included in the document. As for production, the numbers were taken from the OICA website for each year observed.
This work was guided by the existing alliances in the summary whose 19 automakers accounted in particular for approximately 85% of the world production of vehicles according to OICA (2016) in 2013. Nevertheless, the author supplemented the guide with links that were incomplete through Google searches and links to sites that were also dedicated to the industry, such as automaker, Bloomberg, Automotive News, Just-Auto, and Wikipedia. However, the author preferred to assign the last day of each year as the reference date for the alliances in force in that year instead of the dates of March, November and December assigned by the magazine and respective each year of analysis. Direct visits to the official websites of the automakers were also carried out.
The 1359 arcs collected were divided into four major categories and assigned to a particular relationship between two actors arranged in a row in an edge list format, and each category represents a distinct governance structure. The four main categories are related to: 1) ownership or cross-shareholding, 2) joint ventures, 3) manufacturing contracts, and 4) technology alliances and shares.
Regarding each governance structure, the bonds were categorized and henceforth treated as ESO (equity stake owned) for the correspondence of ownership of one actor's actions against another. The direction of the alliance is understood by the interpretation: "Actor A is the property of Actor B"; T&PA for the matching of alliances between two actors that aim at the joint creation/purchase of technologies or parts for vehicles by generating a bidirectional loop or the acquisition of a technology on the one hand. The direction of the alliance is understood by the interpretation: "Actor A acquired technology or parts of Actor B"; CA (contract assembly) that corresponds to alliances between two actors for the purpose of starting the manufacture and/or operations of selling a vehicle together. The direction of the alliance is understood by the interpretation: "Actor A had his vehicles produced in factories of Actor B"; and JV (joint venture) that corresponds to the union of two actors with the purpose of creating a new company that serves certain strategic purposes. The direction of the alliance is understood by the interpretation: "Actor A is a joint venture owned by Actors Bs."
It should be emphasized here that the relations that specify ownership such as ESO and JV will have a less volatile financial meaning as interpretative in their directionality. The idea according to Table 1 is that Nissan corresponds to immobilized money from Renault since the first is owned by the second. The same analogy applies to the company NMKV Ltd., whose organization is considered as immobilized money of the two companies, presenting topological directionality whose contextual interpretation is also "Actor A is property and immobilized money of Actor B."
For the T&PA and CA relations, the money flow has a more literal interpretation, in which it considers merely the directionality based on the idea of who did the service or bought the technology of who, and then there is a flow of money among the automakers.
Consequently, the collected data were considered directional and dichotomous, suitable for use through binary and non-symmetric adjacency matrices, whose values of each cell (x_ij) will alternate between 0 and 1 by the absence or presence respectively of an alliance between the actors iej for each matrix or network interface level. Unlike the population used in Madhavan, Koka and Prescott (1998), whose research encompassed the entire world steel industry, at first the present study was guided by the similar sample established in Sacomano Neto et al. (2016) of 26 automakers.
However, in this work, according to the Guide to Global Automotive Partnerships, in 2011 there were 20 companies analyzed, and in the following two years, there were 19 automakers. The guide no longer considered Porsche due to Volkswagen's acquisition of the automaker in mid-2012. It is emphasized here that, even by the difficulty in gaining access to contracts established between companies, alliances are inserted or removed from the guide when announced in the great specialized media on the respective date of the announcement and not the effective date of the contract.
The network was visualized through the sociograms created through NodeXL, and the data analysis was performed in the UCINET 6 and was initiated by the creation of non-symmetric adjacency matrices in a multiplex network for each year, by transferring the data arranged in the format edge list of Microsoft Excel 2013 software for UCINET. These multiplexes networks will allow the creation of the respective sociograms each year, with the graphic visualization of the actors, subgroups and relations in the same digraph.
Prior to the beginning of the analyzes, the matrices containing each four relationships will be aggregated and summed into a non-symmetric valued matrix for each year, whose cell of a relation x_ij can assume values from 0 to 4, where 0 is the absence of alliance between two actors and 4 is the existence of the 4 alliances between the same actors. These weighted relations are beneficial since they do not generate the loss of information when analyzed by the algorithms used in this work. In this way, the indegree metric, as well as the Louvain algorithm, will be applied to the relations without loss of information of both directionality for actors and groups and weight for the actors. Group metrics are not implemented for weighted matrices.
Concerning the correlation analyzes and tests of statistical significance, they were performed in the Software Package for the Social Sciences, more commonly known as SPSS version 23. The statistical procedures used here and available in SPSS are three: the product-moment correlation coefficient of Pearson, Spearman's rank correlation coefficient and non-exact Monte Carlo permutation tests.
Permutation tests are an excellent tool to ensure statistical significance in inference tests for data collected from relations and have less bias for both small samples and p-value calculation. Berry, Johnston and Mielke Jr. (2014) offer a more comprehensive and broad detailing.
From the perspective of the study by Blythe, Mcgrath and Krackhardt (1995), it is possible to visualize some characteristics of the actors in sociograms initially. From 2011 to 2012 an approach between PSA and GM, and a move to a more central position in the network mainly of automakers like Nissan, Fiat, Mitsubishi, Suzuki and FAW. In contrast, the Toyota and Subaru actors were in slightly more peripheral positions.
Regarding the changes observed from 2012 to 2013, an approach of Mitsubishi was observed with the actors Nissan and Renault, as opposed to the estrangement between Ford and Mazda. Nissan moved into an even more central position, keeping the same movement as the previous year, as well as the American Ford moved away from the periphery and approached the Japanese in a growing centrality and the German Daimler.
Nonetheless, Toyota was more centrally positioned compared to the previous year, but the PSA was established in a less central portion of the network, as opposed to last year. The Honda, Hyundai and SAIC actors did not change their location positions in very peripheral parts of the networks, nor did they approach relevantly any of the analyzed actors.
Based on the assumption that the analyzed network observes the cash flow of each relationship between each pair of actors, the Indegree metrics saw in Table 2 are indicators of the actors’ money inflow not determined by the amount, but instead by the number of observed relationships.
Actors like Daimler, GM, Renault and Fiat have high values of indegree, especially the first automaker. The German company has a high indegree value in comparison to others because it has 17 ESO relationships out of its 31 totals. In contrast, GM has a more heterogeneous formation in its metric, with 10 JV and 8 ESO including its total value.
The year 2012 did not show many changes compared to the previous year. It is possible to observe the automakers that had a higher metric compared to the other actors, only Fiat suffered a significant change, losing 3 units in the indegree metric. These three relationships correspond primarily to the bankruptcy of the automaker Saab Automobile that had a relation of acquisition of powertrains of Fiat.
Nevertheless, the sale of SEVEL Nord's stake in PSA, the non-renewal of the transmission contract for the French company, the abandonment of the joint venture between Fiat and Sollers Group were the causes that led to the fall in the metric. On the other hand, the incorporation of CNH Industrial by Fiat provided an increase in the metric. The automakers Daimler, GM and Renault maintained high values of indegree.
In 2013, Table 2 presents the values of the indegree metrics for the actors. The indegree metric has Daimler as the exponent again since it has a value of 32. Besides, GM, Renault, Ford and Fiat assemblers have values above 20 units. Daimler increased its metric of indegree by 1 because in 2013 it formed an alliance with Ford, Nissan and Renault for the joint development of hydrogen fuel cells. Chrysler, FAW, Hyundai, SAIC and Subaru maintained low indegree values, with Hyundai in particular ending an alliance with Chrysler in the production of Dodge Attitude in Indian and Korean factories of the Korean automaker.
Figure 1 shows the network formed with the subgroups identified for the three years, where the color of the nodes corresponds to the actor group, the node size corresponds to that actor's indegree in the year, and the thickness of the ties illustrates the weight of the relation between the pair of actors. In the first year, 12 groups were identified according to the algorithm resulting in a maximized modularity of Q = 0.667. The Indegree metrics of each group are presented in Table 3.
Thus, for 2011, 11 groups of the 12 totals will be exhibited, since one of the subgroups formed housed only the three Renault Pars, Iran Khodro Co. and SAIPA Group, without the participation of one of the 20 principal actors. It is relevant to state here that the metrics of these subgroups are calculated using all the actors belonging to the network within each subgroup, and not only the separate actors.
As can be seen from Table 3, some companies known to be partners in the automotive industry were relocated to the same subgroup in the network, such as the Ford and Mazda groups, Nissan and Renault, and Chrysler and Fiat. The automakers Mitsubishi, PSA, Honda, BMW and Hyundai were not allocated to any of the other major players. In each group there are 14, 18, 31, 22 and 21 actors respectively to each assembler who ended up isolated in the analysis performed.
As can be seen also from Figure 1, the network configured in the year 2012 presents some characteristics at first glance distinct from the 2011 network concerning the subgroups formed. First, the Louvain algorithm found 10 subgroups in the maximum modularity of Q = 0.661, and again a subgroup formed by the same three actors did not contain any of the major assemblers, being removed from both the statistical analyzes and from Table 3.
In this network, the Honda, Hyundai and BMW assemblers were again allocated to subgroups whose actors out of the 19 taken as reference by the guide were not selected to share one of the 10 groups identified. Thus, the groups formed by the aforementioned automakers contain 30, 26 and 21 actors respectively against 31, 21 and 22 in 2011, with the most-rated actor in the Honda group being GAC Mitsubishi Motors, the five most in the Hyundai group were China Motor Corporation, FJMG Motor, Fujian Benz Automotive, Fujian Motors Group and Soueast Motor and the lesser actor in the BMW group was Inokom Co., which was allocated to the Mazda and Ford group.
The year of 2012 presented two groups similar to the previous year. For groups that presented different configurations, the first one is group 4, which in 2012 presents PSA as a new member of the subgroup. This introduction of PSA can be understood by the alliance initiated by them in 2012, in which the American automaker first acquired 7% of the shares of the French company and started strategies of development and acquisition of technologies and parts already in 2012, and the sharing of platforms soon.
The second subgroup identified that presented changes was the group 5, now composed by Mitsubishi. This approximation between the automakers, which will be maintained for the year 2013, can be conceived as a close relationship between the Japanese and the established relationship of Renault-Nissan that culminated in 2016 with the final alliance between the three, with Nissan acquired 34% of Mitsubishi shares. It can be observed in 2012 that the alliances of T&PA and CA among the Japanese automakers were maintained. These alliances include the joint development of electric vehicles such as MiniCAB MiEV and platform sharing for the development of Mitsubishi Proudia, Lancer and eK, as well as the manufacture of the Nissan Dayz.
The last group for analysis whose composition was changed corresponds precisely to the allocation of the Suzuki assembler that in 2012 belongs to the group of Volkswagen, but in 2011 was assigned to the group of the Japanese Subaru and Toyota, and the Chinese FAW. In 2010, Volkswagen acquired approximately 19% of the shares of the Japanese automaker, and Suzuki acquired 1.49% of German shares.
Regarding the year 2013, the algorithm identified 10 subgroups with a maximum displayed modularity of Q = 0.660. This year compared to the previous year there were no changes in the subgroups regarding the main assemblers and the same subgroup identified over the last two years with three actors was removed, leaving 9 groups once again for analysis.
Although the algorithm has identified subgroups whose main assembler was allocated equally to 2012, 8 actors were assigned to different groups according to the algorithm: Automotive Fuel Cell Cooperation, Berjaya Corporation, Fuso Kamaz Trucks, GAC Fiat Automobiles, GM Powertrain Poland, Inokom Corporation, Mitsubishi Fuso and Tofas. A feature of Louvain's method already pointed out is the non-identification of overlapping communities, avoiding the allocation of the same actor to more than one subgroup.
Regarding the metrics shown in Table 3, the centralities displayed in the results were not significantly changed, firstly by the same principal actors occupying the same groups and finally the allocation of only 8 actors to different groups in the last two years, modifying without much impact the centralities of groups.
The correlations and statistical significance for the years 2011, 2012 and 2013, corresponding to Table 4, show that among the variables analyzed, the one that presented the highest correlation with the metric of indegree was the revenue. First, the associations between them had a moderate to strong effect in all observed years, being statistically significant for the three years analyzed, particularly in Spearman in the correlation between revenue and indegree with the p-value lower than 0.005 in 2011. All other tests of significance between the two variables obtained p-value lower than 0.05.
Pearson	,548	〖",0121" 〗^"*" Pearson	,478	〖",0389" 〗^"*" Pearson	,490	〖",0338" 〗^"*"
Spearman	,603	〖",0046" 〗^"**" Spearman	,478	〖",0401" 〗^"*" Spearman	,482	〖",0371" 〗^"*"
This means that, according to the first hypothesis that actors with greater indegree tend to have greater attributes of production, revenue or profit, there is a positive association of moderate to strong between the inflow of money from the main actors of the network and their respective revenues, implying that automakers that have greater cash flow inflows tend to have higher revenues. Nevertheless, particularly for Spearman in the year of 2011, a robust monotonic relationship between the indegree variable and the production variable can be observed, as well as a moderate monotonic relation between the centrality metric and the corporate profit.
In the specific case of this work, the statistical significance presented between the respective variables above are pointing out that the correlations are significantly different from 0 and that there is a respectively linear or monotonic relation for Pearson and Spearman among the variables analyzed, rejecting the null hypothesis of absence of correlation. It should be noted that the lower the p-value, the more robust is the researcher's decision to state that the result of the statistical test under analysis was not due to randomness from the data.
Spearman	,530	,0973	Spearman	,639	,0718	Spearman	,731	〖",0306" 〗^"*"
Pearson	,694	〖",0124" 〗^"*" Pearson	,873	〖",0009" 〗^"***" Pearson	,894	〖",0009" 〗^"***"
Spearman	,511	,1116	Spearman	,941	〖",0006" 〗^"***" Spearman	,966	〖",0003" 〗^"****"
About the results of the correlations and tests of significance for the actors in the subgroups presented in Table 5, a strong positive relationship between revenue and the centrality of indegree, especially in the last two years, can be observed again with the p-value for Spearman in 2013 below 0.0005.
These results point mainly to a strong similarity between the last two variables of the subgroups formed by automotive industry automakers, demonstrating that the subgroups with the most considerable cash flow tend to have higher revenues.
The researcher points out here that the value of α selected for both tests is 5%, causing a maximum probability of 5% if the type 1 error is committed in each analysis, that is, affirming that there is a correlation between the observed data when in reality the variables are not correlated.
The main objectives of this work were the exploratory analysis of automakers in the global automotive sector between 2011 and 2013, especially in the structural and the comparative aspects: how the actors are organized and the assessment of similarities among the actors and groups’ indegree centrality, and the production, revenue and profit attributes.
Under a general analysis and according to the 20 actors analyzed in the first year and 19 in the subsequent years, the centrality metrics allowed to evaluate the centrality of the main automakers in the network, recognizing very central actors like Fiat, Daimler and GM, while actors more peripherals were pointed out, such as SAIC, FAW, Subaru and Hyundai. In addition, the configuration of the relationship patterns in the networks allowed us to find different subgroups, in the first year a total of 12 subgroups, and in the subsequent years a total of 10 subgroups according to results in Garcia-Pont and Nohria (2002) and in a more similar in Sacomano Neto et al. (2016).
With the removal of a subgroup for the following analysis, the centralities of the groups were also analyzed, and more central or peripheral groups were identified. In general, the evaluation has resulted in the year 2011 in groups 5 and 7, in 2012 and 2013 in groups 4 and 5 as the most central. On the other hand, the most peripheral groups correspond to groups 1 and 3 in 2011 and 2012, and finally 1, 6 and 3 in 2013. The identifications of both the actors and the most central groups in the indegree metric allowed the two hypotheses to be tested. The results support the hypotheses formulated, pointing in particular to a similarity between the revenue and the metric of indegree centrality concerning the relationships collected, as can be observed in the works discussed in the meta-analysis in Wang et al. (2015). The main automakers in the global automotive industry, whose inflow of financial resources is larger, tend to have higher revenues for all observed years.
Nevertheless, the groups formed by these automakers whose inflow of financial resources is larger, also tend to have higher revenue. As the analysis performed was merely a measure of similarity and statistical significance, it is not possible to establish a causal relationship between the variables, and it is possible to inverse the interpretation that actors and groups that have higher revenues tend to obtain greater input flow of financial resources.
The author emphasizes here that the base that guided the data collected for this research lacks several relationships and does not have a temporal coherence with its formations, establishment and closure, being necessary the search for additional information and relations for each presented alliance. Also, it is important to highlight the flexibility with which alliances were given both in the magazine guide and in the surveyed sites, since alliances that were set up in these media as a joint venture were technically an alliance of technology or parts. On the other hand, alliances that were considered as manufacturing contracts or technology and parts were configured as joint ventures.
In reference to the measures of actors and groups centrality carried out, it would be useful to analyze not only the main automakers selected by the guide of the magazine Automotive News, but all the actors belonging to the network. Nonetheless, actors' attribute collection could be extended to a more substantial number of organizations, so that the similarities between the correlations could be verified for a general network trend, not just for the selected actors.
It could be considered a work that analyzes the different structures of governance, seeking more central actors or the formation of subgroups for a particular relation; Nohria and Garcia-Pont (1991), however, did not consider the importance of the relationship established by the organizations. It is pointed here that the three software considered for the creation of networks, Gephi, Node XL and NetDraw, did not have tool for visualization of the multiplexes networks, being restricted the exposure of only one relation in each dyad.
Finally, this work contributed in the theoretical aspect in the creation and treatment of directional networks and multiplexes, and in the identification and evaluation of the centrality of actors and subgroups. Through these points, it was possible to analyze the directionality of a relationship involved in the alliances, as well as to analyze the position of the actors and mainly of the subgroups. The use of the Louvain method made it possible to use the directionality and the weights of the relations as preponderant factors in the delimitation of the communities.
Regarding empirical contribution, research can help managers in the composition of the network of alliances in which the company finds the interest. This composition makes it possible to evaluate the positioning, influence and groupings of organizations, collaborating in strategic decision processes such as the selection of future partners or alliances.
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