Community structure in the World Trade Network based on communicability distances

Paolo Bartesaghi1, Gian Paolo Clemente2, Rosanna Grassi1
1Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Milan, Italy
2Department of Mathematics for Economic, Financial and Actuarial Sciences, Università Cattolica del Sacro Cuore, Milan, Italy

Tóm tắt

In this paper, we investigate the mesoscale structure of the World Trade Network. In this framework, a specific role is assumed by short- and long-range interactions, and hence by any suitably defined network-based distance between countries. Therefore, we identify clusters through a new procedure that exploits Estrada communicability distance and the vibrational communicability distance, which turn out to be particularly suitable for catching the inner structure of the economic network. The proposed methodology aims at finding the distance threshold that maximizes a specific quality function defined for general metric spaces. Main advantages regard the computational efficiency of the procedure as well as the possibility to inspect intercluster and intracluster properties of the resulting communities. The numerical analysis highlights peculiar relationships between countries and provides a rich set of information that can hardly be achieved within alternative clustering approaches.

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Tài liệu tham khảo

Abeysinghe T, Forbes K (2005) Trade linkages and output-multiplier effects: a structural var approach with a focus on asia. Rev Int Econ 13(2):356–375

Barigozzi M, Fagiolo G, Mangioni G (2011) Identifying the community structure of the international-trade multi-network. Physica A 390(11):2051–2066

Blöchl F, Theis FJ, Vega-Redondo F, Fisher EO (2011) Vertex centralities in input-output networks reveal the structure of modern economies. Phys Rev E 83(4):046127

Bozzo E (2013) The Moore–Penrose inverse of the normalized graph Laplacian. Linear Algebra Appl 439(10):3038–3043. https://doi.org/10.1016/j.laa.2013.08.039

Cepeda-López F, Gamboa-Estrada F, León C, Rincón-Castro H (2019) The evolution of world trade from 1995 to 2014: a network approach. J Int Trade Econ Dev 28(4):452–485

Cerqueti R, Ferraro G, Iovanella A (2018) A new measure for community structure through indirect social connections. Expert Syst Appl 114:196–209

Cerqueti R, Clemente GP, Grassi R (2019) A network-based measure of the socio-economic roots of the migration flows. Soc Indic Res. https://doi.org/10.1007/s11205-018-1883-6

Chang C, Liao W, Chen Y, Liou L (2016) A mathematical theory for clustering in metric spaces. IEEE Trans Netw Sci Eng 3(1):2–16

Clemente GP, Cornaro A (2019) A novel measure of edge and vertex centrality for assessing robustness in complex networks. Soft Comput 24:3687–13704

Clemente GP, Fattore M, Grassi R (2018) Structural comparisons of networks and model-based detection of small-worldness. J Econ Interact Coord 13(1):117–141

De Benedictis L, Tajoli L (2011) The world trade network. World Econ 34(8):1417–1454

De Benedictis L, Tajoli L (2016) Comparative advantage and centrality in the world network of trade and value added: an analysis of the Italian Position. Riv Polit Econ 66(3):537–554

Dées S, Saint-Guilhem A (2011) The role of the united states in the global economy and its evolution over time. Empir Econ 41(3):573–591

Del Rio-Chanona RM, Grujic J, Jeldtoft Jensen H (2017) Trends of the world input and output network of global trade. PLoS ONE 12(1):1–14. https://doi.org/10.1371/journal.pone.0170817

Ellens W, Spieksma F, Van Mieghem P, Jamakovic A, Kooij R (2011) Effective graph resistance. Linear Algebra Appl 435:2491–2506

Estrada E (2012) Complex networks in the euclidean space of communicability distances. Phys Rev E 85:066122. https://doi.org/10.1103/PhysRevE.85.066122

Estrada E (2012) The structure of complex networks: theory and applications. Oxford University Press, Oxford

Estrada E, Hatano N (2008) Communicability in complex networks. Phys Rev E 77:036111. https://doi.org/10.1103/PhysRevE.77.036111

Estrada E, Hatano N (2009) Communicability graph and community structures in complex networks. Appl Math Comput 214(2):500–511. https://doi.org/10.1016/j.amc.2009.04.024

Estrada E, Hatano N (2010) Resistance distance, information centrality, node vulnerability and vibrations in complex networks. Springer, London

Estrada E, Hatano N (2010) A vibrational approach to node centrality and vulnerability in complex networks. Phys A Stat Mech Appl 389(17):3648–3660. https://doi.org/10.1016/j.physa.2010.03.030

Estrada E, Rodriguez-Velazquez JA (2005) Subgraph centrality in complex networks. Phys Rev E Stat Nonlinear Soft Matter Phys 71:056103. https://doi.org/10.1103/PhysRevE.71.056103

Fagiolo G (2007) Clustering in complex directed networks. Phys Rev E. https://doi.org/10.1103/physreve.76.026107

Fagiolo G, Reyes J, Schiavo S (2008) On the topological properties of the world trade web: a weighted network analysis. Physica A 387(15):3868–3873

Fagiolo G, Reyes J, Schiavo S (2010) The evolution of the world trade web: a weighted-network analysis. J Evolut Econ 20(4):479–514

Fagiolo G, Squartini T, Garlaschelli D (2013) Null models of economic networks: the case of the world trade web. J Econ Interact Coord 8(1):75–107

Fagiolo G, Victor JN, Lubell M, Montgomery A (2015) The international trade network: empirics and modeling. In: The Oxford handbook of political networks, pp. 173–193

Fan Y, Ren S, Cai H, Cui X (2014) The state’s role and position in international trade: a complex network perspective. Econ Model 39:71–81

Ferraz de Arruda G, Luiz Barbieri A, Rodríguez PM, Rodrigues FA, Moreno Y, da Fontoura Costa L (2014) The role of centrality for the identification of influential spreaders in complex networks. Phys Rev E 90:032812

Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174

Fortunato S, Hric D (2016) Community detection in networks: a user guide. Phys Rep 659:1–44

Garlaschelli D, Loffredo MI (2004) Fitness-dependent topological properties of the world trade web. Phys Rev Lett 93(18):188701

Garlaschelli D, Loffredo MI (2005) Structure and evolution of the world trade network. Physica A 355(1):138–144

Garlaschelli D, Di Matteo T, Aste T, Caldarelli G, Loffredo MI (2007) Interplay between topology and dynamics in the world trade web. Eur Phys J B 57(2):159–164

Giudici P, Spelta A (2016) Graphical network models for international financial flows. J Bus Econ Stat 34(1):128–138

Gutman I, Xiao W (2004) Generalized inverse of the Laplacian matrix and some applications. Bulletin (Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathématiques), pp 15–23

Hausmann R, Hidalgo CA, Bustos S, Coscia M, Simoes A, Yildirim MA (2014) The atlas of economic complexity: mapping paths to prosperity. MIT Press, Cambridge

Kali R, Reyes J (2007) The architecture of globalization: a network approach to international economic integration. J Int Bus Stud 38(4):595–620

Klein D, Randic M (1993) Resistance distance. J Math Chem 12:81–95. https://doi.org/10.1007/BF01164627

Kozmetsky G, Yue P (2012) Global economic competition: today’s warfare in global electronics industries and companies. Springer, New York

Kuznetsova NV, Kocheva EV, Matev NA (2016) The analysis of foreign trade activities of Russia and Asia-Pacific region. Int J Econ Financ Issues 6(2):736–744

Lancichinetti A, Fortunato S (2009) Community detection algorithms: a comparative analysis. Phys Rev E 80(5):056117

Lee C, Tenneti S, Eun DY (2019) Transient dynamics of epidemic spreading and its mitigation on large networks. CoRR arXiv:1903.00167

Li X, Jin YY, Chen G (2003) Complexity and synchronization of the World trade web. Physica A 328(1–2):287–296

Lidth Van, de Jeude J, Di Clemente R, Caldarelli G, Saracco F, Squartini T (2019) Reconstructing mesoscale network structures. Complexity. https://doi.org/10.1155/2019/5120581

Newman ME (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69(6):066133

Newman ME, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113

Nicolini C, Bordier C, Bifone A (2017) Community detection in weighted brain connectivity networks beyond the resolution limit. Neuroimage 146:28–39

Piccardi C, Tajoli L (2012) Existence and significance of communities in the world trade web. Phys Rev E 85:066119. https://doi.org/10.1103/PhysRevE.85.066119

Piccardi C, Tajoli L (2018) Complexity, centralization, and fragility in economic networks. PLoS ONE 13(11):1–13. https://doi.org/10.1371/journal.pone.0208265

Rattigan MJ, Maier M, Jensen D (2007) Graph clustering with network structure indices. In: Proceedings of the 24th international conference on Machine learning. ACM, pp 783–790

Reyes J, Schiavo S, Fagiolo G (2008) Assessing the evolution of international economic integration using random walk betweenness centrality: the cases of East Asia and Latin America. Adv Complex Syst 11(05):685–702

Schiavo S, Reyes J, Fagiolo G (2010) International trade and financial integration: a weighted network analysis. Quant Finance 10(4):389–399

Serrano MA, Boguñá M (2003) Topology of the world trade web. Phys Rev E 68(1):015101

Serrano MA, Boguñá M, Vespignani A (2007) Patterns of dominant flows in the world trade web. J Econ Interact Coord 2(2):111–124

Smith DA, White DR (1992) Structure and dynamics of the global economy: network analysis of international trade 1965–1980. Soc Forces 70(4):857–893

Snyder D, Kick EL (1979) Structural position in the world system and economic growth, 1955–1970: a multiple-network analysis of transnational interactions. Am J Sociol 84(5):1096–1126

Traag VA, Aldecoa R, Delvenne J (2015) Detecting communities using asymptotical surprise. Phys Rev E 92(2):022816

Tzekina I, Danthi K, Rockmore DN (2008) Evolution of community structure in the world trade web. Eur Phys J B 63(4):541–545

Van Mieghem P, Devriendt K, Cetinay H (2017) Pseudoinverse of the Laplacian and best spreader node in a network. Phys Rev E. https://doi.org/10.1103/PhysRevE.96.032311

Van Berkum S (2013) Trade effects of the EU-Morocco Association Agreement. 2013-070. LEI, onderdeel van Wageningen UR

Varela LM, Rotundo G, Ausloos M, Carrete J (2015) Complex network analysis in socioeconomic models. In: Complexity and geographical economics. Springer, pp 209–245

Wang X, Pournaras E, Kooij R, Van Mieghem P (2014) Improving robustness of complex networks via the effective graph resistance. Eur Phys J B 87(9):221

Ward MD, Ahlquist JS, Rozenas A (2013) Gravity’s rainbow: a dynamic latent space model for the world trade network. Netw Sci 1(1):95–118

Wilhite A (2001) Bilateral trade and small-world networks. Comput Econ 18(1):49–64

WTO (2017) World trade statistical review. Technical report. World Trade Organizations

Zhu Z, Cerina F, Chessa A, Caldarelli G, Riccaboni M (2014) The rise of China in the international trade network: a community core detection approach. PLoS ONE 9(8):e105496