Identification and visualization of clusters using network theory methods: The case of the Greek production system

Foutakis, Dimitris Article Identification and visualization of clusters using network theory methods: The case of the Greek production system Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Foutakis, Dimitris (2025) : Identification and visualization of clusters using network theory methods: The case of the Greek production system, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 1, pp. 1-31, https://doi.org/10.3390/economies13010015 This Version is available at: https://hdl.handle.net/10419/329295 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Academic Editors: Periklis Gogas and Theophilos Papadimitriou Received: 2 December 2024 Revised: 24 December 2024 Accepted: 27 December 2024 Published: 11 January 2025 Citation: Foutakis, D. (2025). Identification and Visualization of Clusters Using Network Theory Methods: The Case of the Greek Production System. Economies,13(1), 15. https://doi.org/10.3390/ economies13010015 Copyright: © 2025 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Identification and Visualization of Clusters Using Network Theory Methods: The Case of the Greek Production System Dimitris Foutakis Department of Surveying and Geoinformatics Engineering (Serres), International Hellenic University, 62124 Serres, Greece; [email protected] or [email protected] Abstract: The interest in clusters in the economy and regional space, which has persisted for nearly three decades, has reignited the understanding of the economy as a system of interdependencies between industries. Although the concept of clusters can be traced back to contributions dating from the early 20th century, they have become a central focus of regional development policies in recent decades, as they have been linked to enhancements of innovation, the knowledge economy, and ultimately, territorial competitiveness. Arguably, the most effective and comprehensive way to present the systemic nature of the economy is through input–output tables. The main feature of these tables, on which this work is based, is that they describe the relationships and flows between industries (or products) during the production process. These fundamental relationships among the industries in the production system are depicted in the inter-industry (and intra-industry) transaction matrix of an economy’s input–output tables. To analyze these relationships, we use network theory, in the context of which the transaction matrix can be seen as the adjacency matrix of a directed, weighted graph (or network) with loops. In this study, clusters are identified for the case of Greece, using two different approaches based on the modularity of the network, utilizing the 2010 input–output tables for this country. As a result, five clusters of industries that structure the country’s production system across 62 industries are identified, which are also presented through graphical visualizations. Keywords: clusters; input–output tables; graph/network theory; production system; Greece 1. Introduction The aim of this article is to present a method for identifying and visualizing clusters, using the production system of Greece as a case study. Although the concept of clusters appeared in economic theory as “industrial districts” (Marshall,1964, Chapter 10) as early as the late 19th century (1890), it re-emerged in work by Porter (1998) and others at the end of the 20th century with a rather ambiguous content. 1 However, the geographical level of reference remains unclear: it could refer to a neighborhood in a metropolitan area, a region (however defined), a country, or even groups of countries (Martin & Sunley,2003). Furthermore, ambiguity exists regarding the types of industries involved, whether they are similar or complementary, as well as the nature of their relationships. Despite these uncertainties, clusters are considered crucial elements of regional policy within various versions of new regionalism (Amin & Thrift,1995;Amin,1999;Cook,2002;Cook & Morgan, 1998;Florida,1995;Morgan & Nauwelaers,1999;Morgan,1997;Storper,1997), as they are seen as key drivers for promoting innovation, the “knowledge economy”, and ultimately, the competitiveness of regions and countries. Economies 2025,13, 15 https://doi.org/10.3390/economies13010015 Economies 2025,13, 15 2 of 31 Regardless of any conceptual ambiguities or weaknesses, the discussion regarding clusters brings to the forefront the issue of the division of labor and the interdependent nature of economic activity. In this regard, the overall economic activity functions as a system of interdependent, separate economic activities carried out by independent economic units linked through exchange relationships, either as inputs or as outputs of intermediate or final goods, means of production, or services. The intensity of these relationships is not uniformly distributed among industries but tends to concentrate around specific industries or groups of industries and has a dynamic and changing character. The geographical scale of industries’ concentration, which is addressed by contemporary cluster theory, remains an open research question. In this paper, a methodological approach for identifying and visualizing clusters is first presented. Then, in Section 3, this approach is applied, using Greece as a case study, based on the analysis of the transaction matrix from the 2010 Greek input–output tables (Eurostat,2013), using tools from graph/network theory. In this section, the results of applying this methodology are also presented, which leads to the identification of five clusters in the Greek production system. Section 4features a detailed discussion about the composition and internal function of these clusters, and the paper then proceeds to Section 5.2 2. Method for the Identification and Visualization of Clusters, and Data Handling 2.1. Identification of Clusters Identifying subdivisions or clusters within a network (graph) is both conceptually and computationally complex, with numerous methods and algorithms proposed for solving this problem (Fortunato,2010). In the context of input–output tables, the existence of functional subdivisions has been known about since the 1950s and 1960s (see Leontief, 1986), taking forms such as strategic industries, industry hierarchies, or cohesive groupings (clusters). 3 The methodological approach of this study views the input–output table as a graph (or network), a perspective that aligns with a scientific trend from the early 2000s, which established network science as a separate field focused on real-world networks (social, technological, biological, cognitive) (Newman,2010;Barabási,2014).4 The transaction matrix of the input–output table is treated as the adjacency matrix of a directed, weighted network (with or without loops), allowing the use of the network’s topological characteristics and associated quantitative data (weights of links). This framework enables the identification of subgroups or clusters based on the transactions between industries. The search for cohesive structures within a complex network, described by a matrix or graph, is a problem in matrix and graph theory, which is known as partitioning. The goal is to divide the adjacency matrix into submatrices (subgraphs) in a way that minimizes the links between them, forming groupings with more internal links (edges) than external ones. This problem is very challenging to solve practically, even in its simplest form, which is the bisection (splitting into two equal parts) of a graph. In this seemingly straightforward case, the graph, i.e., its corresponding adjacency matrix, must be divided into two subgraphs (submatrices) with an equal number of nodes (vertices). However, the number of possible ways to bisect the graph is approximately 2 (n+1) / √ n, where nis the number of nodes/vertices (Newman,2010, p. 359; Barabási,2014, Chapter 9, pp. 8–9). This means that the number of solutions increases exponentially with the increase in the number of nodes of the graph, with the result being that when the number of nodes of the graph exceeds a few dozen, finding and evaluating solutions is computationally infeasible in practice. If the number of divisions is not predetermined, the number of possible solutions increases even Economies 2025,13, 15 3 of 31 faster than exponentially, as described by the Bell number, which approximates the number of partitions (Barabási,2014, Chapter 9, p. 9; Fortunato,2010, p. 87). There are numerous approaches to solving the problem of network division and numerous corresponding algorithms, as detailed in an extensive review by Fortunato (2010). The large number of methods and algorithms can be attributed not only to the computational complexity of the problem—being NP-hard, which undoubtedly contributes to the development of many algorithms—but also to the inherent ambiguity in defining what constitutes a cohesive subgroup. This ambiguity leads to multiple, sometimes slightly varied definitions and terms being used to describe the same phenomenon (or ontology). In the literature, terms such as graph partitioning,modules,clusters, and communities are used interchangeably or alternatively (Newman,2010;Fortunato,2010;Fortunato & Castellano, 2012;Barabási,2014). The term “communities” is the most recent and is often preferred in approaches that identify substructures without predefining the number or other characteristics of these subgroups. The algorithms developed from such an approach emerged primarily during the early 2000s, driven significantly by the involvement of physicists in the field. These “physicists entered the game, bringing in their tools and techniques: spin models, optimization, percolation, random walks, synchronization, etc., became ingredients of new original algorithms” (Fortunato & Castellano,2012, p. 492). In contrast, earlier algorithms, which relied on the prior specification of certain parameters for the subdivisions of a graph or network under study, were primarily the result of research within the domain of social network analysis (Wasserman & Faust,1994;Scott,2000). K-means clustering and hierarchical clustering are the most commonly used algorithms in social network analysis. The first has the serious limitation that the number of clusters to be formed must be specified in advance. The second does not have this limitation but “it does not provide any a way to discriminate between the many partitions obtained by the procedure, and to choose that or those that better represent the community structure of the graph” (Fortunato & Castellano, 2012, p. 498). This differentiation among algorithms enables an initial classification of the various approaches based on a seemingly “technical” criterion. Specifically, these methods are divided into (a) those that predetermine the number of partitions or the size of the groupings (number of nodes) to be formed, or the degree centrality (number of edges or links) for each node in the subgraphs created, and (b) those that partition the graph without any prior specification of the number, size, or other characteristics of the subdivisions (Newman, 2010, pp. 354–358). The first class of methods rely on a framework of assumptions or a model regarding the graph’s structure, expressed through parameters that define the number and features of the partitions. In contrast, the second approach does not make any assumptions about the graph’s structure or the number or size of its cohesive structures and relies solely on the graph’s inherent data, producing a solution (or solutions) by optimizing an evaluation index derived from comparisons with a “null model”. This null model is a random graph that maintains certain structural characteristics of the graph under study (Fortunato, 2010, p. 86). 5 It is crucial to note that in both approaches, partitioning is based solely on topological features. This second method uses an index called the network modularity, which compares the links (edges) within each subgroup (cluster/community) in a proposed partition to the number expected if the network was random (Newman & Girvan,2004). Mathematically, Economies 2025,13, 15 4 of 31 modularity quantifies this comparison (Fortunato & Castellano,2012, p. 493; Barabási,2014, Chapter 9, p. 20) as follows: Q=∑nc c=1"lc m−dc 2m2# where n c is the total number of subgroups, l c is the number of edges within subgroup c,m is the total number of edges in the network, and d c is the total degree of the nodes within the same subgroup c. This mathematical formulation clarifies that modularity depends on the difference between two quantities: the first is the ratio of the edges within a subgroup to the total number of edges in the network, and the second is the ratio of the expected edges within the same subgroup to the total number of edges in the network, assuming that the network’s nodes are randomly connected but retain their original degree. In this study, the method of maximizing modularity is used to identify clusters within Greece’s production system. Despite having some disadvantages, this method has a significant advantage: it does not require any preconceived judgment or assumption about the network’s structure. This is unlike many established methods from social network analysis and hierarchical clustering, which depend on such assumptions. However, this method is not without its problems: (a) it misclassifies subgroups that are smaller than a certain resolution limit, as it cannot distinguish them from the null model (Fortunato & Castellano,2012, p. 501), and (b) rather than having a single optimal maximum, there is often a range of near-optimal solutions forming a plateau instead of a unique peak (Barabási,2014, Chapter 9, p. 24). Nevertheless, algorithms based on modularity maximization are generally trusted by the scientific community and it is considered that “modularity offers a first principle understanding of a network’s community structure” (Barabási,2014, Chapter 9, p. 24). Modularity always takes values less than one. Positive values (Q> 0) indicate a good partition, with higher values representing better results. A value of zero (Q= 0) means there is no significant clustering, while negative values (Q< 0) imply that the random graph’s internal connections are better than those of the given subdivision, indicating an unacceptable partition. This subdivision is considered unacceptable because a random graph yields better results. The index takes strongly negative values when each node in the network is treated as a separate subgroup. Generally, negative modularity values indicate the absence of meaningful subgroups or communities within the network structure. This is a clear signal that the division does not exhibit the expected community characteristics, implying that the network lacks cohesive internal groupings. In practice, acceptable modularity values range from 0.3 to 0.7, although higher values may occasionally appear (Newman & Girvan,2004, p. 7). Maximizing modularity is known to be an NP-hard problem, meaning that it can only be approximated using heuristic and approximation algorithms (Fortunato & Castellano, 2012, p. 500). Fortunato (2010), in his comprehensive review of community detection in graphs, discusses various classes of heuristic algorithms, such as greedy, genetic, simulated annealing, spectral, and tabu search, each offering different levels of success depending on the network’s size and complexity. To divide Greece’s production system into clusters, two different modularity-based approaches were used: (a) the Louvain method reported by Blondel et al. (2008) and (b) the Girvan–Newman method modified by Arenas et al. (Girvan & Newman,2002;Newman, 2004;Arenas et al.,2007,2008). Both methods are tailored to directed, weighted networks and use the modularity index to evaluate the network partitions they produce, ultimately proposing an optimal division into clusters.6 Economies 2025,13, 15 5 of 31 The first method, Louvain, aggregates each node with others in the network, recalculating the modularity at each step until the division that maximizes the modularity is found (Blondel et al.,2008, pp. 3–4). The second method successively splits the network by removing edges with the highest betweenness and recalculates the modularity at every stage. These two methods differ in the algorithms they use to calculate modularity. Given that the computation of modularity falls into the category of NP-hard problems (Fortunato & Castellano,2012, p. 500), it can only be addressed using stochastic, heuristic optimization algorithms. The Louvain method employs a greedy algorithm (Fortunato, 2010, pp. 101–102 ), while the modified Girvan–Newman method, as adapted by Arenas et al., uses a different optimization approach called tabu search. Even though both methods use the modularity as the criterion for evaluating network partitions, they fundamentally differ in their strategies to achieve partitioning and in how they optimize the modularity. The Louvain method was implemented using Pajek network analysis software 4.10 (Mrvar & Batagelj,2016). Arenas et al.’s method—a modified version of the Girvan–Newman method—was implemented using Radatools software suite 4.0 (Gómez & Fernández,2016). Thus, even though both approaches seek to maximize the modularity, their methodologies and algorithmic implementations are distinct, affecting their performance and results in terms of network partitioning. 2.2. Visualization of Results The visualization of graphs/networks, and consequently, of clusters, is an inherent advantage and key feature of network analysis. For graphs with a relatively limited number of nodes (vertices), such as a few dozen, representation can be relatively simple, often taking the form of a grid. Another option is a circular diagram, which offers an aesthetically appealing result (Krzywinski et al.,2009;Crnovrsanin et al.,2014). However, for graphs or networks with several dozen or even hundreds of nodes, these methods become impractical. In such cases, visualization involves linking nodes/vertices with lines where links exist. The challenge in these more complex networks is that there is no single way to represent the network graphically (Di Battista et al.,1994, p. 236). Instead, there are theoretically infinite ways to arrange the nodes and edges, as shown in the following figure. For instance, even a simple graph with four vertices and five edges can be represented in at least three equally valid ways (Figure 1). These representations maintain the relationships between nodes (vertices), as indicated by the connecting lines (edges/links), but result in visually different diagrams. Economies 2025, 13, x 5 of 32 stage. These two methods differ in the algorithms they use to calculate modularity. Given that the computation of modularity falls into the category of NP-hard problems (Fortunato & Castellano, 2012, p. 500), it can only be addressed using stochastic, heuristic optimization algorithms. The Louvain method employs a greedy algorithm (Fortunato, 2010, pp. 101–102), while the modified Girvan–Newman method, as adapted by Arenas et al., uses a different optimization approach called tabu search. Even though both methods use the modularity as the criterion for evaluating network partitions, they fundamentally differ in their strategies to achieve partitioning and in how they optimize the modularity. The Louvain method was implemented using Pajek network analysis software 4.10 (Mrvar & Batagelj, 2016). Arenas et al.’s method—a modified version of the Girvan–Newman method—was implemented using Radatools software suite 4.0 (Gómez & Fernández, 2016). Thus, even though both approaches seek to maximize the modularity, their methodologies and algorithmic implementations are distinct, affecting their performance and results in terms of network partitioning. 2.2. Visualization of Results The visualization of graphs/networks, and consequently, of clusters, is an inherent advantage and key feature of network analysis. For graphs with a relatively limited number of nodes (vertices), such as a few dozen, representation can be relatively simple, often taking the form of a grid. Another option is a circular diagram, which offers an aesthetically appealing result (Krzywinski et al., 2009; Crnovrsanin et al., 2014). However, for graphs or networks with several dozen or even hundreds of nodes, these methods become impractical. In such cases, visualization involves linking nodes/vertices with lines where links exist. The challenge in these more complex networks is that there is no single way to represent the network graphically (Di Battista et al., 1994, p. 236). Instead, there are theoretically infinite ways to arrange the nodes and edges, as shown in the following figure. For instance, even a simple graph with four vertices and five edges can be represented in at least three equally valid ways (Figure 1). These representations maintain the relationships between nodes (vertices), as indicated by the connecting lines (edges/links), but result in visually different diagrams. Figure 1. Different representations of the same graph. The inherent flexibility in visualizing graphs/networks, and consequently, clusters, introduces subjectivity into how graphs/networks are represented. This characteristic of graphs certainly qualifies the value of immediacy and ease in understanding the relationships depicted through a graphical representation. The final visualization of a graph is not a single, “objective” mathematical outcome but rather a result of a creative design and, ultimately, the researcher’s intent. This flexibility can potentially lead to the “misguiding” of the reader (or even the researcher themselves) since it allows for the presentation of data in a way that might emphasize certain aspects of the relationships—which may not be the most important ones—that are described by the graph. This issue has led to the development of a subfield within graph theory focused specifically on visualization. This area addresses two interconnected core concerns: (a) Figure 1. Different representations of the same graph. The inherent flexibility in visualizing graphs/networks, and consequently, clusters, introduces subjectivity into how graphs/networks are represented. This characteristic of graphs certainly qualifies the value of immediacy and ease in understanding the relationships depicted through a graphical representation. The final visualization of a graph is not a single, “objective” mathematical outcome but rather a result of a creative design and, ultimately, the researcher’s intent. This flexibility can potentially lead to the “misguiding” of the reader (or even the researcher themselves) since it allows for the presentation of data Economies 2025,13, 15 6 of 31 in a way that might emphasize certain aspects of the relationships—which may not be the most important ones—that are described by the graph. This issue has led to the development of a subfield within graph theory focused specifically on visualization. This area addresses two interconnected core concerns: (a) aesthetic rules that ensure the readability and understanding of the graph and (b) the creation of algorithms for efficient computer-based graph rendering. The first aspect is directly related to the clarity and interpretability of graphs, while the second focuses on the computational efficiency of algorithms used for visualization. As Di Battista et al. (1999, p. 14) note, “aesthetics specify graphic properties of the drawing that we would like to apply, as much as possible, to achieve readability”. Examples of aesthetic rules include minimizing the crossing of edges, reducing the total diagram area, and ensuring uniformity in the edge length (Di Battista et al.,1999, pp. 15–16). When it comes to algorithms for implementing graph design rules, it should be noted that these are essentially optimization problems that may not be simultaneously solvable and are also computationally difficult (NP-hard). Considering the issue of computational efficiency, it becomes necessary to prioritize the aesthetic criteria for graph layout. As a result, the final output of these algorithms often involves a combination of “approximation strategies and heuristics” (Di Battista et al.,1999, pp. 16–17). Despite the variety of algorithms available for graph drawing, they generally share a common foundation. Many algorithms used to achieve the final layout rely on a force-directed approach, a model inspired by the basic principles of mechanics (Eades,1984). The core idea involves treating the edges (links) as springs, which helps to distribute the nodes (vertices) in a balanced way across a two-dimensional space, such as a computer screen, a printer, or a plotter. Variations of this approach underpin the algorithms used in modern software for social network analysis and specialized mathematical tools. For this article, the Fruchterman and Reingold (1991) algorithm was used, incorporating Lombardi-style curves to aesthetically enhance the diagrams by giving the edges a curved shape (Duncan et al.,2012). The network diagram was created using Gephi ver. 0.901 software (Bastian et al.,2009;Jacomy et al.,2014). The grid-based layout was created using Pajek ver. 4.10 software (Mrvar & Batagelj,2016), and the circular diagram was created with Circos Table Viewer v. 0.63-10 software (Krzywinski et al.,2009). 2.3. Handling of Data The data used in this study were from the domestic input–output table for the year 2010 (product by product) in current basic prices (in millions of EUR). This table originates from the official input–output tables for Greece in 2010 (Eurostat,2013), provided by the European Statistical Office (Eurostat). 7 The classification of products and industries follows the Classification of Products by Activity-CPA 2008 (European Union,2008) for goods and services, and the NACE Rev. 2 Statistical classification of economic activities in the European Community (Eurostat,2008) for economic activities. The Eurostat data categorize 65 products/industries: 64 according to CPA/NACE classifications plus 1 additional industry, “L68A: Imputed rents of owner-occupied dwellings”. For simplification, three industries with zero or exceptionally low values in the transactions matrix were removed, as well as five negative values that were economically meaningless, because they reversed the direction of flows and impacts. These values appeared in the output of two industries: N78 (“Employment services”) and I (“Accommodation and food services”). Specifically, the negative values amounted to EUR 0.48 million for N78 (across three entries) and EUR 1.06 million for I (across two entries). These were adjusted to zero, with a negligible overall impact, as the matrix’s total transactions amount to approximately EUR 111 billion, resulting in an effect of around 0.01‰. Economies 2025,13, 15 7 of 31 Additionally, three industries with negligible or zero presence were completely removed: U (“Services provided by extraterritorial organizations and bodies”), L68A (“Imputed rents of owner-occupied dwellings”), and T (“Services of households as employers; undifferentiated goods and services produced by households for own use”). These industries made no contribution to the added value and did not show any significant transactions. Following the adjustments mentioned previously, the dimensions of the matrix became 62 × 62 (reduced from the 65 × 65 version officially published by Eurostat), containing a total of 3844 entries. Of these, 416 entries (10.8%) were zeros, compared to 780 zeros (18.5%) in the original matrix. Further simplification eliminated very small transaction values, which were replaced with zero. As a result, the number of zero entries increased to 2328 (60.6% of the total). It should be noted that this adjustment preserved 98% of the original sum of values from the 62 × 62 matrix before the interventions, amounting to EUR 109.077 billion out of EUR 111.614 billion. This modified matrix was subsequently used for cluster identification and visualization using the method described earlier. In the presentation and commentary on the results, industries appearing in clusters were categorized by technology level and knowledge intensity. This categorization followed Eurostat’s guidelines (see Eurostat,2016). The intensity of research and technological development (R&D) was used to classify two-digit manufacturing industries, using R&D expenditures as a percentage of gross value added. Four categories emerged: High Technology (HT), Medium–High Technology (MHT), Medium–Low Technology (MLT), and Low Technology (LT). For service industries, the criterion was the percentage of employees in the corresponding two-digit economic activity industries who have a tertiary education degree. These service industries were classified in line with the two main categories in manufacturing (i.e., high and low technology) into two primary groups: Knowledge-Intensive Services (KIS) and Less-Knowledge-Intensive Services (LKIS). Furthermore, the first category (KIS) was subdivided into Knowledge-Intensive Market Services (KI_m_S), High Technology Knowledge-Intensive Services (Ht_KIS), Knowledge-Intensive Financial Services (KI_f_S), and Other Knowledge-Intensive Services (O_KIS). Less-Knowledge-Intensive Services were subdivided into Less-Knowledge-Intensive Market Services (LKI_m_S) and Other Less-Knowledge-Intensive Services (O_LKIS). It should be emphasized that all the previous technology and knowledge intensity categories exclude the three industries of the primary sector as well as certain secondary sector industries, namely Mining (B), Electricity–Gas (D35), Water Supply (E36), Waste Management (E37–E39), and Construction (F). Due to the absence of an “official” classification from Eurostat, we designated these industries as “traditional” and marked them with the label “TR” in the related tables. In the tables and commentary that follow, industries are identified using the NACE Rev. 2 classification codes. The description of the industries used for presentation purposes is a shortened version of their official description, which is provided in Appendix A. 3. Results 3.1. The Clusters and the Reliability of the Division The outcome of dividing the transaction matrix into five clusters is shown in Table 1. It is important to note that, using both methods for maximizing the modularity (the Louvain method and the Girvan–Newman method modified by Arenas et al.), the initial division produced a sixth “cluster”, which consisted of the “isolated” industry H53 Postal Services. After a separate analysis of its connections and to achieve a more coherent presentation of the results, this industry was integrated into the “Mega-cluster”. Due to the large size of Economies 2025,13, 15 8 of 31 the Mega-cluster (24 industries), incorporating Postal Services as its 25th member did not affect its overall character. Table 1. Clusters in the production system of Greece, 2010. Code Description of Cluster and Industry Code Description of Cluster and Industry A. AGRICULTURE–TOURISM D. KNOWLEDGE–EDUCATION (cont.) 1. A01 Agriculture 6. M72 Research and development 2. A02 Forestry 7. M73 Advertising 3. A03 Fishing 8. M74_M75 * Other scientific activities 4. C10–C12 Food–Beverages 9. N78 Employment activities 5. C33 Repair/installation of machinery 10. P85 Education 6. I Accommodation–Restaurants 11. R90-R92 Creative activities—Gambling 7. S94 Membership organizations 12. R93 Sports–Recreation 8. S96 Personal services E. MEGA-CLUSTER B. ENERGY–TRANSPORT 1. C13–C15 Textiles–Apparel 1. B Mining 2. C17 Paper 2. C19 Petroleum products 3. C20 Chemicals 3. D35 Electricity–Gas 4. C21 Pharmaceuticals 4. E36 Water supply 5. C22 Plastic products 5. H49 Land transport 6. C26 Computers–Electronics 6. H50 Water transport 7. C29 Motor vehicles 7. H51 Air transport 8. C30 Other transport equipment 8. H52 Warehousing 9. C31_C32 Furniture–Other manufacturing 9. N77 Rental/leasing activities 10. E37–E39 Waste management C. CONSTRUCTION 11. G45 Trade and repair of motor vehicles 1. C16 Wood 12. G46 Wholesale trade 2. C23 Non-metallic mineral products 13. G47 Retail trade 3. C24 Basic metals 14. H53 ** Postal activities 4. C25 Metal products 15. K64 Financial services 5. C27 Electrical equipment 16. K65 Insurance 6. C28 Machinery 17. K66 Other financial services 7. F Construction 18. L68 Real estate 8. M71 Architects–Engineers 19. M69_M70 Legal, accounting, management activities D. KNOWLEDGE–EDUCATION 20. N79 Travel agencies 1. C18 Printing 21. N80-N82 Security, services to buildings 2. J58 Publishing 22. O84 Public administration, defense 3. J59_J60 Cinema–Television 23. Q86 Health 4. J61 Telecommunications 24. Q87_Q88 Social care 5. J62_J63 Computer–Information services 25. S95 * Repair of computers and household goods Source: Modified transaction matrix. Data processed with the Louvain and Arenas et al. methods. (*) These industries were appointed by the Louvain method: (a) M74_M75 to cluster E, (b) S95 to cluster C. (**) The industry H53 in the original divisions of both methods was a separate “cluster”. Differences between the two methods were observed in only two cases: 1. Industry M74_M75 Other Scientific Services: The Louvain method placed it in the “Mega-cluster”, while the Arenas et al. method (i.e., the modified G-N method) placed it in the “Knowledge–Education” cluster. 2. Industry S95 Repair of Computers and Household Appliances: The Louvain method placed it in the “Construction” cluster, while the Arenas et al. method placed it in the “Mega-cluster”. Economies 2025,13, 15 15 of 31 prominence of A01 Agriculture, C10–C12 Food–Beverages, I Accommodation–Restaurants, and S94 Membership Organizations, which primarily receive outputs from industries I and C10–C12. Economies 2025, 13, x 15 of 32 directed toward international markets, particularly those of industries A03, A01, and C10C12, and I, although for the latter (tourism from abroad), this is not captured in the input– output tables. From the circular diagram (Figure 5), it is apparent that this cluster’s structure revolves around three key industries, namely Agriculture, Food–Beverages, and Accommodation– Restaurants, with the other industries playing a complementary role. This structure is illustrated differently in the network diagram (Figure 6), where the importance of each industry is depicted by the size of the network nodes (vertices) and labels. This importance is measured using the eigenvector centrality index (“PageRank”), and the thickness of the lines represents the volume of transactions. The network diagram highlights the prominence of A01 Agriculture, C10–C12 Food–Beverages, I Accommodation–Restaurants, and S94 Membership Organizations, which primarily receive outputs from industries I and C10–C12. Figure 5. Circular diagram of the Agriculture–Tourism cluster. Figure 6. Network diagram of the Agriculture–Tourism cluster. Figure 5. Circular diagram of the Agriculture–Tourism cluster. Economies 2025, 13, x 15 of 32 directed toward international markets, particularly those of industries A03, A01, and C10C12, and I, although for the latter (tourism from abroad), this is not captured in the input– output tables. From the circular diagram (Figure 5), it is apparent that this cluster’s structure revolves around three key industries, namely Agriculture, Food–Beverages, and Accommodation– Restaurants, with the other industries playing a complementary role. This structure is illustrated differently in the network diagram (Figure 6), where the importance of each industry is depicted by the size of the network nodes (vertices) and labels. This importance is measured using the eigenvector centrality index (“PageRank”), and the thickness of the lines represents the volume of transactions. The network diagram highlights the prominence of A01 Agriculture, C10–C12 Food–Beverages, I Accommodation–Restaurants, and S94 Membership Organizations, which primarily receive outputs from industries I and C10–C12. Figure 5. Circular diagram of the Agriculture–Tourism cluster. Figure 6. Network diagram of the Agriculture–Tourism cluster. Figure 6. Network diagram of the Agriculture–Tourism cluster. Finally, from a technological perspective, as shown in Table 3, this is a low-technology and less-knowledge-intensive cluster. Only C33 Repair/Installation of Machinery is a medium–low technology industry, while the others are either traditional (the three primary sector industries) or low-technology and less-knowledge-intensive industries. 4.3. Energy–Transport Cluster The Energy–Transport cluster (Figures 7and 8) consists of nine industries: B Mining, C19 Petroleum Products, D35 Electricity–Gas, E36 Water Supply, H49 Land Transport, H50 Economies 2025,13, 15 16 of 31 Water Transport, H51 Air Transport, H52 Warehousing, and N77 Rental and Leasing Activities. As shown in Table 4, this cluster could alternatively be described as the Export cluster, as it accounts for more than half of the country’s exports (52.5%). However, considering that all the transport and logistics services along with the energy production industries are found in this cluster, it is appropriate to name it the Energy–Transport cluster. Economies 2025, 13, x 17 of 32 D35 Electricity–Gas, while H50 Water Transport receives inputs mainly from H52 Warehousing and C19 Petroleum Products, with minimal outputs. Figure 7. Circular diagram of the Energy–Transport cluster. Figure 8. Network diagram of the Energy–Transport cluster. Considering the overall characteristics of the Energy–Transport cluster and the industries that comprise it, this cluster emerges as a critical component of the production system, primarily due to its strong orientation toward the international market. Several of its industries are internationally competitive, notably H50 Water Transport, C19 Petroleum Products, and H52 Warehousing. Figure 7. Circular diagram of the Energy–Transport cluster. Table 4. Energy–Transport cluster: main economic characteristics. NACE Code Description Technology Transactions Inside Cluster Empl. (%) Demand (%) Added Value Exports Output Input (%) Technical Coefficient (%) Extroversion B Mining TR 0.98 0.30 0.3 0.1 0.3 47.5 0.4 12.4 C19 Petroleum products MLT 0.56 0.48 0.2 3.8 1.0 14.5 10.7 31.3 D35 Electricity–Gas TR 0.42 0.72 0.6 1.8 2.3 53.8 0.5 2.2 E36 Water supply TR 0.10 0.50 0.2 0.2 0.2 48.1 0 0 H49 Land transport LKI_m_S 0.19 0.38 2.4 2.1 1.5 43.3 0.5 3.0 H50 Water transport KI_m_S 0.41 0.47 0.7 6.2 3.7 47.0 37.4 96.0 H51 Air transport KI_m_S 0.28 0.54 0.2 0.6 0.3 28.1 1 18.2 H52 Warehousing LKI_m_S 0.80 0.45 0.9 0.3 0.6 42.0 1.9 27.6 N77 Rental/leasing activities LKI_m_S 0.38 0.16 0.1 0.1 0.3 51.1 0.1 3.4 Total Energy–Transport Cluster 0.50 5.6 15.3 10.2 38.3 52.5 39.5 This cluster has moderate cohesion, with the value of the inter-industry transactions divided equally between internal and external transactions (50–50). At the industry level, Mining (B),Electricity–Gas (D35),Petroleum Products (C19), and Warehousing (H52) display a clear “introversive” orientation, meaning that most of their transaction value occurs with other industries within the cluster rather than with the rest of the production system, as indicated in the relevant columns (Outputs, Inputs) of the table. The remaining industries in the cluster exhibit varying degrees of volume of external transactions, interacting more with industries outside the cluster. Economies 2025,13, 15 17 of 31 Economies 2025, 13, x 17 of 32 D35 Electricity–Gas, while H50 Water Transport receives inputs mainly from H52 Warehousing and C19 Petroleum Products, with minimal outputs. Figure 7. Circular diagram of the Energy–Transport cluster. Figure 8. Network diagram of the Energy–Transport cluster. Considering the overall characteristics of the Energy–Transport cluster and the industries that comprise it, this cluster emerges as a critical component of the production system, primarily due to its strong orientation toward the international market. Several of its industries are internationally competitive, notably H50 Water Transport, C19 Petroleum Products, and H52 Warehousing. Figure 8. Network diagram of the Energy–Transport cluster. The Energy–Transport cluster makes a relatively low contribution to employment (5.6%) and has a low technical coefficient of added value (38.3%). This indicates that this cluster is characterized by low added value or, conversely, a high intensity of intermediate inputs. Most of the industries in this cluster are classified as low-technology and lessknowledge-intensive. Only industries H50 Water Transport and H51 Air Transport are classified as knowledge-intensive (KI_m_S), while the C19 Petroleum Products industry is medium–low technology (MLT). In Figures 7and 8, the cluster’s structure is illustrated, which is centered around Mining (B),Petroleum Products (C19),Electricity–Gas (D35), and Transportation (primarily maritime H50 but also land H49). Complementing this core structure are industries such as H52 Warehousing,H51 Air Transport,N77 Rental/Leasing Activities, and E36 Water Supply. The D35 Electricity–Gas industry serves as a supplier for all the other industries within the cluster, as do C19 Petroleum Products and N77 Rental and Leasing Activities. The B Mining industry primarily supplies C19 Petroleum Products and D35 Electricity–Gas, while H50 Water Transport receives inputs mainly from H52 Warehousing and C19 Petroleum Products, with minimal outputs. Considering the overall characteristics of the Energy–Transport cluster and the industries that comprise it, this cluster emerges as a critical component of the production system, primarily due to its strong orientation toward the international market. Several of its industries are internationally competitive, notably H50 Water Transport,C19 Petroleum Products, and H52 Warehousing. 4.4. Construction Cluster The Construction cluster (Figures 9and 10) is composed of eight industries, including six manufacturing industries: C16 Wood,C23 Non-Metallic Products,C24 Basic Metals,C25 Metal Products,C27 Electrical Equipment, and C28 Machinery. It also includes F Construction and M71 Architects–Engineers from the service sector. This cluster is particularly cohesive, with over two-thirds of its transactions (0.68) occurring internally (Table 5). Most industries, except for C28 Machinery and M71 Architects–Engineers, engage in internal transactions in terms of either outputs or inputs. Its name underlines the central role of the Construction industry in the cluster. Economies 2025,13, 15 18 of 31 Economies 2025, 13, x 18 of 32 4.4. Construction Cluster The Construction cluster (Figures 9 and 10) is composed of eight industries, including six manufacturing industries: C16 Wood, C23 Non-Metallic Products, C24 Basic Metals, C25 Metal Products, C27 Electrical Equipment, and C28 Machinery. It also includes F Construction and M71 Architects–Engineers from the service sector. This cluster is particularly cohesive, with over two-thirds of its transactions (0.68) occurring internally (Table 5). Most industries, except for C28 Machinery and M71 Architects–Engineers, engage in internal transactions in terms of either outputs or inputs. Its name underlines the central role of the Construction industry in the cluster. Figure 9. Circular diagram of the Construction cluster. The Construction cluster is the smallest of the five clusters in terms of production volume, contributing only 7.3% of the total gross value added (GVA). Nearly half of this output (3.6%) comes solely from the Construction (F) industry. The other half comes from the other five industries, each contributing less than 1% of the total GVA of the production system. The added value technical coefficient is the lowest among all five clusters (33.5%) due to the exceptionally low values across its industries, some of the lowest in the production system. Generally, apart from the Construction industry, this cluster consists of relatively small industries. This is reflected in the modest share of total employment (12.7%) and demand (10.7%) of the cluster, with the Construction industry accounting for the majority (7.5% in employment and 8.1% in demand). Despite the small size of its industries, the Construction cluster has a notable export contribution (11.9% of total exports of the production system), mainly from its six manufacturing industries. The C24 Basic Metals Figure 9. Circular diagram of the Construction cluster. Economies 2025, 13, x 19 of 32 industry leads exports (5.2%), followed by the C27 Electrical Equipment industry (2.1%), with the remaining four Manufacturing industries contributing 2.9%. This export strength is evident in the high export index (Extroversion) of most Manufacturing industries in the cluster. Table 5. Construction cluster: main economic characteristics. NACE Code Description Technology Transactions Inside Cluster Empl. (%) Demand (%) Added Value Exports Output Input (%) Technical Coefficient (%) Extroversion C16 Wood LT 0.67 0.54 0.5 0.0 0.2 29.7 0.1 3.1 C23 Non-metallic mineral products MLT 0.96 0.34 0.6 0.2 0.7 50.5 0.8 11.1 C24 Basic metals MLT 0.83 0.52 0.5 0.8 0.6 24.4 5.2 43.5 C25 Metal products MLT 0.65 0.48 1.2 0.4 0.7 33.3 0.7 6.4 C27 Electrical equipment MHT 0.62 0.47 0.3 0.4 0.3 42.8 2.1 67.9 C28 Machinery MHT 0.31 0.42 0.2 0.5 0.3 50.1 1.3 42.9 F Construction TR 0.50 0.64 7.5 8.1 3.6 31.8 1.4 2.5 M71 Architects–Engineers ΚΙ_m_S 0.58 0.09 1.5 0.3 0.9 35.4 0.3 2.3 Total Construction Cluster 0.68 12.2 10.7 7.3 33.5 11.9 10.9 Figure 10. Network diagram of the Construction cluster. Technologically, most industries in the Construction cluster are of low or medium– low technology (LT, MLT), apart from M71 Architects–Engineers, which is knowledgeintensive (ΚΙ_m_S), while the Construction (F) industry is traditional (T). However, the central role of the Construction industry enables it to activate other industries in the cluster through its backward linkages, 65% of which are internal. Most industries, with the internal forward linkages ranging from 58% to 96%, are interconnected within the cluster. This means that changes in the demand for the Construction industry can propagate through inter-industry relationships and stimulate demand for higher-technology and knowledge-intensive industries, such as C27 Electrical Equipment (medium–high technology), C28 Machinery (medium–high technology), and M71 Architects–Engineers (knowledge-intensive). Figure 10. Network diagram of the Construction cluster. Economies 2025,13, 15 19 of 31 Table 5. Construction cluster: main economic characteristics. NACE Code Description Technology Transactions Inside Cluster Empl. (%) Demand (%) Added Value Exports Output Input (%) Technical Coefficient (%) Extroversion C16 Wood LT 0.67 0.54 0.5 0.0 0.2 29.7 0.1 3.1 C23 Non-metallic mineral products MLT 0.96 0.34 0.6 0.2 0.7 50.5 0.8 11.1 C24 Basic metals MLT 0.83 0.52 0.5 0.8 0.6 24.4 5.2 43.5 C25 Metal products MLT 0.65 0.48 1.2 0.4 0.7 33.3 0.7 6.4 C27 Electrical equipment MHT 0.62 0.47 0.3 0.4 0.3 42.8 2.1 67.9 C28 Machinery MHT 0.31 0.42 0.2 0.5 0.3 50.1 1.3 42.9 F Construction TR 0.50 0.64 7.5 8.1 3.6 31.8 1.4 2.5 M71 Architects–Engineers KI_m_S 0.58 0.09 1.5 0.3 0.9 35.4 0.3 2.3 Total Construction Cluster 0.68 12.2 10.7 7.3 33.5 11.9 10.9 The Construction cluster is the smallest of the five clusters in terms of production volume, contributing only 7.3% of the total gross value added (GVA). Nearly half of this output (3.6%) comes solely from the Construction (F) industry. The other half comes from the other five industries, each contributing less than 1% of the total GVA of the production system. The added value technical coefficient is the lowest among all five clusters (33.5%) due to the exceptionally low values across its industries, some of the lowest in the production system. Generally, apart from the Construction industry, this cluster consists of relatively small industries. This is reflected in the modest share of total employment (12.7%) and demand (10.7%) of the cluster, with the Construction industry accounting for the majority (7.5% in employment and 8.1% in demand). Despite the small size of its industries, the Construction cluster has a notable export contribution (11.9% of total exports of the production system), mainly from its six manufacturing industries. The C24 Basic Metals industry leads exports (5.2%), followed by the C27 Electrical Equipment industry (2.1%), with the remaining four Manufacturing industries contributing 2.9%. This export strength is evident in the high export index (Extroversion) of most Manufacturing industries in the cluster. Technologically, most industries in the Construction cluster are of low or medium–low technology (LT, MLT), apart from M71 Architects–Engineers, which is knowledge-intensive (KI_m_S), while the Construction (F) industry is traditional (T). However, the central role of the Construction industry enables it to activate other industries in the cluster through its backward linkages, 65% of which are internal. Most industries, with the internal forward linkages ranging from 58% to 96%, are interconnected within the cluster. This means that changes in the demand for the Construction industry can propagate through inter-industry relationships and stimulate demand for higher-technology and knowledgeintensive industries, such as C27 Electrical Equipment (medium–high technology), C28 Machinery (medium–high technology), and M71 Architects–Engineers (knowledge-intensive). 4.5. Knowledge–Education Cluster The Knowledge–Education cluster is composed of 12 industries; one is a Manufacturing industry and 11 are from the Service sector (Figures 11 and 12). Its name highlights two primary characteristics: the economic significance of the Education (P85) industry and the high concentration of service industries in this cluster, with 11 out of a total of 21 knowledge-intensive service industries in the production system being in this cluster. Alternatively, it could also be called the Knowledge–Communication cluster, as at least six of its industries are involved in producing, supporting, and managing traditional mass and newer Internet-based interactive communication media. These include C18 Printing, J58 Publishing,J59_J60 Cinema–TV,J61 Telecommunications,J62_J63 Computer–Information Services, and M73 Advertising. Additionally, this cluster incorporates activities from the R90-R92 Creative Activities and Gambling industry, which include the R90 Creative Arts and Entertainment industry. Economies 2025,13, 15 20 of 31 Economies 2025, 13, x 21 of 32 coefficient arises from the extremely high values in certain industries. Most industries in this cluster use minimal intermediate inputs, and in some cases, such as J61 Telecommunications, J58 Publishing, and R90–R92 Creative Activities–Gambling, a significant portion of their transactions are intra-industry. Figure 11. Circular diagram of the Knowledge–Education cluster. Figure 12. Network diagram of the Knowledge–Education cluster. On the other hand, M73 Advertising (9.8%) and M72 Research and Development (27.1%) have relatively high volumes of inputs. This cluster performs particularly poorly in Figure 11. Circular diagram of the Knowledge–Education cluster. Economies 2025, 13, x 21 of 32 coefficient arises from the extremely high values in certain industries. Most industries in this cluster use minimal intermediate inputs, and in some cases, such as J61 Telecommunications, J58 Publishing, and R90–R92 Creative Activities–Gambling, a significant portion of their transactions are intra-industry. Figure 11. Circular diagram of the Knowledge–Education cluster. Figure 12. Network diagram of the Knowledge–Education cluster. On the other hand, M73 Advertising (9.8%) and M72 Research and Development (27.1%) have relatively high volumes of inputs. This cluster performs particularly poorly in Figure 12. Network diagram of the Knowledge–Education cluster. Many of these industries rely on telecommunications services provided by J61 Telecommunications as well as on the production and services of C18 Printing and J58 Publishing to create and manage mass communication and entertainment. These industries represent the majority of the so-called “creative industries”, which employ the members of the “creative class” (Florida,2012, pp. 35–62). Ultimately, the name Knowledge–Education cluster was Economies 2025,13, 15 21 of 31 preferred because of the economic structure of the cluster and the significance of knowledge production and dissemination, which is primarily a result of educational processes. One distinguishing feature of the Knowledge–Education cluster, as shown in Table 6, is its relatively low cohesion (0.39) compared to the other four clusters in the production system. It also makes the smallest contribution to demand (10.5%) and is the second smallest in terms of employment (12.3%) and gross value added (13.4%). The significance of P85 Education is evident in its impact on these indicators, as it accounts for approximately half or more of the cluster’s total value in each case. Aside from Education, no other industry makes a notable contribution to employment, with Education itself representing 7.5%. Table 6. Knowledge–Education cluster: main economic characteristics. NACE Code Description Technology Transactions Inside Cluster Empl. (%) Demand (%) Added Value Exports Output Input (%) Technical Coefficient (%) Extroversion C18 Printing LT 0.26 0.04 0.6 0.0 0.2 44.6 0.0 0.2 J58 Publishing O_KIS 0.43 0.43 0.4 1.2 1.3 62.0 0.4 4.1 J59_J60 Cinema–Television Ht_KIS 0.77 0.59 0.4 0.5 0.3 30.5 0.3 5.1 J61 Telecommunications Ht_KIS 0.37 0.58 0.7 1.9 2.7 63.6 0.7 3.5 J62_J63 Computer–Information services Ht_KIS 0.32 0.49 0.5 0.4 0.6 64.0 0.8 17.3 M72 Research and development Ht_KIS 0.83 0.50 0.2 0.2 0.1 27.1 0.2 12.5 M73 Advertising KI_m_S 0.34 0.49 0.4 0.1 0.2 9.8 0.3 4.5 M74_M75 Other scientific activities KI_m_S 0.11 0.52 0.5 0.2 0.5 47.5 0.3 7.0 N78 Employment activities KI_m_S 0.65 0.30 0.1 0.0 0.1 92.8 0.0 0.0 P85 Education O_KIS 0.27 0.48 7.5 4.8 5.7 94.5 0.1 0.2 R90-R92 Creative activities—Gambling O_KIS 0.64 0.94 0.7 1.2 1.6 79.8 0.1 0.7 R93 Sports–Recreation O_KIS 0.62 0.49 0.4 0.1 0.1 34.9 0.0 0.2 Total Knowledge–Education Cluster 0.39 12.3 10.5 13.4 66.0 3.2 3.3 This is a cluster that operates with a very high technical coefficient of added value (66%), the highest among the five clusters and above the overall production system average (55.6%). According to the detailed industry-specific data in Table 6, this high coefficient arises from the extremely high values in certain industries. Most industries in this cluster use minimal intermediate inputs, and in some cases, such as J61 Telecommunications,J58 Publishing,and R90–R92 Creative Activities–Gambling, a significant portion of their transactions are intra-industry. On the other hand, M73 Advertising (9.8%) and M72 Research and Development (27.1%) have relatively high volumes of inputs. This cluster performs particularly poorly in exports (3.2%), with the highest export-contributing industry, J62_J63 Computer–Information Services, contributing only 0.8% to the total exports of the production system. Similarly, this cluster has a low external orientation (Extroversion) index (3.3%), with nearly all its industries, except for M72 Research and Development (12.5%) and J62_J63 Computer–Information Services (17.3%), having significantly lower values than the production system average (11.1%). This indicates that while the cluster is composed of knowledge-intensive services, it lacks an export orientation. The exceptions are M72 Research and Development and J62_J63 Computer– Information Services, which show potential for exports. 4.6. Mega-Cluster The Mega-cluster, as suggested by its name, is the largest cluster in the production system in terms of almost all aspects except for exports (Table 7). It consists of 25 industries in total: 10 from the secondary sector (8 of which are manufacturing) and 15 from the service sector. It includes some of the largest industries by employment, such as G47 Retail Trade (12.3%),O84 Public Administration (8.5%), and Q86 Health (4.7%), as well as some of the strongest in terms of demand and added value, like L68 Real Estate (10.3% and 15.1%, respectively), O84 Public Administration–Defense (9.9% and 8.7%), and G46 Wholesale Trade (6.3% and 6.0%). Economies 2025,13, 15 22 of 31 Table 7. Mega-cluster: main economic characteristics. NACE Code Description Technology Transactions Inside Cluster Empl. (%) Demand (%) Added Value Exports Output Input (%) Technical Coefficient (%) Extroversion C13–C15 Textiles–Apparel LT 0.83 0.85 1.1 0.8 0.5 42.9 2.9 45.5 C17 Paper LT 0.57 0.85 0.2 0.3 0.2 29.5 0.3 11.1 C20 Chemicals MHT 0.52 0.70 0.3 0.5 0.3 27.6 2.2 45.5 C21 Pharmaceuticals HT 0.97 0.78 0.4 0.5 0.5 58.6 1.9 45.7 C22 Plastic products MLT 0.50 0.79 0.3 0.2 0.1 18.1 1.0 24.9 C26 Computers–Electronics HT 0.37 0.76 0.1 0.1 0.1 58.4 0 0 C29 Motor vehicles MHT 0.87 0.69 0.1 0.1 0.1 48.0 0.1 15.7 C30 Other transport equipment MHT 0.18 0.64 0.2 0.1 0.1 65.0 0.1 14.0 C31_C32 Furniture—other manufacturing LT 0.92 0.52 1.0 0.5 0.3 33.6 0.5 11.7 E37–E39 Waste management TR 0.58 0.40 0.5 0.4 0.7 58.1 0.6 9.4 G45 Trade and repair of motor vehicles LKI_m_S 0.32 0.77 2.0 1.9 2.3 66.4 1.2 6.6 G46 Wholesale trade LKI_m_S 0.38 0.69 3.7 6.3 6.0 46.3 6.2 9.5 G47 Retail trade LKI_m_S 0.40 0.68 12.3 3.3 3.7 55.2 3.2 9.4 H53 Postal activities O_LKIS 0.65 0.83 0.5 0.0 0.3 37.4 0.0 1.1 K64 Financial services KI_f_S 0.61 0.64 1.8 1.2 3.6 69.3 0.8 3.1 K65 Insurance KI_f_S 0.39 0.90 0.4 0.5 0.4 44.6 0.8 18.2 K66 Other financial services KI_f_S 0.62 0.74 0.4 0.0 0.6 76.4 0 0 L68 Real estate LKI_m_S 0.69 0.61 0.1 10.3 15.1 93.2 0 0 M69_M70 Legal, accounting, management activities KI_m_S 0.57 0.62 2.4 0.4 2.1 62.2 0.8 4.5 N79 Travel agencies LKI_m_S 0.58 0.59 0.3 0.4 0.3 31.6 0 0 N80–N82 Security, services to buildings LKI_m_S 0.55 0.53 1.2 0.2 1.7 53.0 0.2 1.2 O84 Public administration, defense, social security O_KIS 1.00 0.59 8.5 9.9 8.7 71.8 0 0 Q86 Health O_KIS 0.86 0.87 4.7 5.5 4.6 67.6 0.1 0.3 Q87_Q88 Social care O_KIS 0.81 0.48 0.9 0.4 0.3 55.8 0 0 S95 Repair of computers and household goods LKI_m_S 0.35 0.77 0.3 0.3 0.4 81.6 0.1 4.8 Total Mega-Cluster 0.53 43.6 44.2 53.2 65.1 23.0 5.6 In terms of exports, the Mega-cluster ranks second (23.0%), but this is largely due to the sheer number of its industries rather than the strength of any individual export industry. It is a cohesive cluster, the third highest in terms of cohesion among the five clusters, with 53% of its transaction volume occurring internally. This cohesion persists despite the cluster having twice or even more than triple the number of industries (25) compared to the other clusters (8 to 12). Almost all of its industries have a transaction index for both inputs and outputs that exceeds 0.5. The relatively high degree of cohesion makes further division attempts unreliable. When the cluster was subjected to the same division process as the overall network (a production system composed of 62 industries), using the same method (modularity optimization algorithms including the Louvain and Arenas et al. based on the modified G-N method), the results were inconsistent. The Louvain method produced three new sub-clusters: one with a single isolated industry (C13-C15 Textiles–Apparel), a second with six industries that could be referred to a “healthcare-pharmaceutical sub-cluster” (including C20 Chemicals,C21 Pharmaceuticals,C22 Plastics,C31_C32 Furniture, and healthcare and social welfare services Q86 Health,Q87_Q88 Social Care), and a third sub-cluster containing the remaining 18 industries. The Arenas et al. method resulted in five sub-clusters, with only the isolated C13-C15 Textiles–Clothing sub-cluster matching the Louvain results. The remaining four sub-clusters varied, with two containing four industries each and two containing nine industries each. The significant variation in the results between the two methods indicates that further division of the Mega-cluster is particularly unreliable. The outcome from the Lou-vain method seems to make more economic sense, as it identifies a grouping centered around healthcare and social welfare services, along with the pharmaceutical industry, drawing in related industries like chemicals and plastics. Additionally, this division has a higher modularity index (Q= 0.2681) compared to the second method (Q= 0.1575). It should be noted, however, that the modularity values in both cases are significantly lower than those for the main division, which were Q= 0.3005 for the Louvain method and Q= 0.2923 for the Arenas et al. method. Overall, these results are insufficient to confidently Economies 2025,13, 15 23 of 31 claim that the production system consists of seven or, even more unlikely, nine clusters. Nevertheless, these findings can guide a better understanding of how the Mega-cluster functions, especially when combined with diagrammatic representations. The diagrams reveal the density of the interand intra-industry relationships within the Mega-cluster, contributing to its relatively high cohesion index. In the circular diagram (Figure 13), the quantitative prominence of the Trade industries (G45,G46,G47) is evident, marked with brown-shaded arcs and connections, both forward and backward. The second most significant group is the Financial sector (K64 Financial Services,K65 Insurance, and K66 Other Financial Services), depicted in gray shades. Business service providers (M69_M70 and N80–N82) and N79 Travel Agencies, marked in shades of blue, form another major group with strong ties to both the Trade and Financial sectors. Economies 2025, 13, x 24 of 32 industry ones, explaining their isolation as individual clusters in the initial production system division and the Mega-cluster sub-division attempts. The network diagram (Figure 14) of the Mega-cluster emphasizes the topological significance of industries rather than the volume of inter-industry relations highlighted in the previous circular chord diagram. In this visualization, as with the corresponding diagrams for the other clusters, the size and placement of the industries (nodes/vertices) indicate their importance or “influence” within the network (cluster). This influence is summarized by the eigenvector centrality (PageRank), which considers both the number and strength of the linkages as well as the significance of the connected industries. Figure 13. Circular diagram of the Mega-cluster. Figure 13. Circular diagram of the Mega-cluster. The L68 Real Estate industry, shown in dark green, also has notable links with Trade and Finance. Public sector industries (O84 Public Administration,Q85 Health, and Q86_Q87 Social Care), shaded in purple, mainly serve as recipients of forward linkages from other industries within the cluster. The linkage between Q86 Health and C21 Pharmaceuticals Economies 2025,13, 15 24 of 31 and C31_C32 Furniture is notable, which justifies their appearance as a separate “healthcarepharmaceutical sub-cluster” in the Louvain results. The Manufacturing industries, marked in red, have a relatively small size but maintain a significant number of inter-industry linkages within the cluster. Lastly, the diagrams show that H53 Postal Activities and C13-C15 Textiles– Apparel have a higher volume of intra-industry linkages compared to inter-industry ones, explaining their isolation as individual clusters in the initial production system division and the Mega-cluster sub-division attempts. The network diagram (Figure 14) of the Mega-cluster emphasizes the topological significance of industries rather than the volume of inter-industry relations highlighted in the previous circular chord diagram. In this visualization, as with the corresponding diagrams for the other clusters, the size and placement of the industries (nodes/vertices) indicate their importance or “influence” within the network (cluster). This influence is summarized by the eigenvector centrality (PageRank), which considers both the number and strength of the linkages as well as the significance of the connected industries. Economies 2025, 13, x 25 of 32 Figure 14. Network diagram of the Mega-cluster. The network diagram of the Mega-cluster reveals three groups of industries: 1. Public Sector Industries: Including O84 Public Administration and Defense and Q86 Health. 2. Trade Industries: Comprising G46 Wholesale Trade, G47 Retail Trade, and G45 Automotive Trade and Repairs. 3. Financial Sector Industries: Consisting of K64 Financial Services and K65 Insurance. The L68 Real Estate industry is less prominent in this network view compared to the previous circular diagram, while the M69_M70 Legal–Accounting Services and N80–N82 Protection and Other Services industries, despite being positioned peripherally, have some influence on the cluster’s dynamics. Notably, C21 Pharmaceuticals and C31_C32 Furniture, located near Q86 Health at the top of the diagram, and the nearby Q86_Q87 Social Care, C20 Chemicals, and C22 Plastics form the “healthcare-pharmaceutical sub-cluster” previously identified. The Mega-cluster exhibits a balance between high-technology and knowledge-intensive industries on the one hand and low-technology and less-knowledge-intensive industries on the other. Specifically, this cluster includes five highand medium–high-technology industries and five lowand low–medium-technology industries (including E37–E39 Waste Management). In the service sector, there are eight knowledge-intensive industries and seven less-knowledge-intensive ones, totaling 13 high-technology and knowledgeintensive industries versus 12 low-technology and less-knowledge-intensive industries. Despite this numerical balance, the outcomes of the cluster favor low-technology and less-knowledge-intensive production. High-technology (HT and MHT) and knowledgeintensive industries (KI_f_S and O_KIS) contribute 21.5% to the total gross value added (GVA) of the production system, compared to 31.7% for low-technology (LT, MLT and TR) and less-knowledge-intensive industries (LKI_m_S and O_LKIS). Similarly, in terms of employment, high-technology (HT and MHT) and knowledge-intensive industries (KI_f_S and O_KIS) account for 20%, while less-intensive ones account for 23.6%. For the overall demand, the figures are 19.2% versus 25%, and for exports, they are 6.8% versus Figure 14. Network diagram of the Mega-cluster. The network diagram of the Mega-cluster reveals three groups of industries: 1. Public Sector Industries: Including O84 Public Administration and Defense and Q86 Health. 2. Trade Industries: Comprising G46 Wholesale Trade,G47 Retail Trade,and G45 Automotive Trade and Repairs. 3. Financial Sector Industries: Consisting of K64 Financial Services and K65 Insurance. The L68 Real Estate industry is less prominent in this network view compared to the previous circular diagram, while the M69_M70 Legal–Accounting Services and N80– N82 Protection and Other Services industries, despite being positioned peripherally, have some influence on the cluster’s dynamics. Notably, C21 Pharmaceuticals and C31_C32 Furniture, located near Q86 Health at the top of the diagram, and the nearby Q86_Q87 Social Care,C20 Chemicals, and C22 Plastics form the “healthcare-pharmaceutical sub-cluster” previously identified. Economies 2025,13, 15 31 of 31 Newman, M. E. J., & Girvan, M. (2004). 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