On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank, hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.

[1]  Martin G. Everett,et al.  Analyzing social networks , 2013 .

[2]  Frank Schweitzer,et al.  Economic Networks: What Do We Know and What Do We Need to Know? , 2009, Adv. Complex Syst..

[3]  Duncan J. Watts,et al.  Six Degrees: The Science of a Connected Age , 2003 .

[4]  Marián Boguñá,et al.  Decoding the structure of the WWW: facts versus sampling biases , 2005, ArXiv.

[5]  Peter Nijkamp,et al.  Accessibility of Cities in the Digital Economy , 2004, cond-mat/0412004.

[6]  Ian T. Foster,et al.  Mapping the Gnutella Network , 2002, IEEE Internet Comput..

[7]  T. Killingback,et al.  Attack Robustness and Centrality of Complex Networks , 2013, PloS one.

[8]  S. Bornholdt,et al.  Scale-free topology of e-mail networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  R. Hanneman Introduction to Social Network Methods , 2001 .

[10]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[11]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[12]  Morten L. Bech,et al.  The topology of Danish interbank money flows , 2008 .

[13]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[14]  Ágnes Lublóy,et al.  Topology of the Hungarian large-value transfer system , 2006 .

[15]  Hideki Takayasu,et al.  Fractal Network derived from banking transaction -- An analysis of network structures formed by financial institutions -- , 2004 .

[16]  Giulia Iori,et al.  Criticality in a model of banking crises , 2001 .

[17]  Vladimir Batagelj,et al.  Exploratory Social Network Analysis with Pajek , 2005 .

[18]  Lada A. Adamic,et al.  Power-Law Distribution of the World Wide Web , 2000, Science.

[19]  Walter E. Beyeler,et al.  The topology of interbank payment flows , 2007 .

[20]  Michael Boss,et al.  Network topology of the interbank market , 2003, cond-mat/0309582.

[21]  Hernán A. Makse,et al.  Influence maximization in complex networks through optimal percolation , 2015, Nature.

[22]  Fan Chung Graham,et al.  A random graph model for massive graphs , 2000, STOC '00.

[23]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[24]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[25]  R. Kitt Economic Decision Making: Application of the Theory of Complex Systems , 2012, 1208.1277.

[26]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[27]  R. Pastor-Satorras,et al.  Generation of uncorrelated random scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[29]  Bruce M. Maggs,et al.  Globally Distributed Content Delivery , 2002, IEEE Internet Comput..

[30]  M. E. J. Newman,et al.  Power laws, Pareto distributions and Zipf's law , 2005 .

[31]  Ian T. Foster,et al.  Mapping the Gnutella Network: Properties of Large-Scale Peer-to-Peer Systems and Implications for System Design , 2002, ArXiv.

[32]  D. Sornette,et al.  Dynamics of book sales: endogenous versus exogenous shocks in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[34]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[35]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[36]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[37]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[38]  Andrei Z. Broder,et al.  Graph structure in the Web , 2000, Comput. Networks.

[39]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[40]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[41]  A. Gibbons Algorithmic Graph Theory , 1985 .

[42]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[43]  J. Doye Network topology of a potential energy landscape: a static scale-free network. , 2002, Physical review letters.

[44]  G. Caldarelli,et al.  A Network Analysis of the Italian Overnight Money Market , 2005 .

[45]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.