Randomizing bipartite networks: the case of the World Trade Web

Within the last fifteen years, network theory has been successfully applied both to natural sciences and to socioeconomic disciplines. In particular, bipartite networks have been recognized to provide a particularly insightful representation of many systems, ranging from mutualistic networks in ecology to trade networks in economy, whence the need of a pattern detection-oriented analysis in order to identify statistically-significant structural properties. Such an analysis rests upon the definition of suitable null models, i.e. upon the choice of the portion of network structure to be preserved while randomizing everything else. However, quite surprisingly, little work has been done so far to define null models for real bipartite networks. The aim of the present work is to fill this gap, extending a recently-proposed method to randomize monopartite networks to bipartite networks. While the proposed formalism is perfectly general, we apply our method to the binary, undirected, bipartite representation of the World Trade Web, comparing the observed values of a number of structural quantities of interest with the expected ones, calculated via our randomization procedure. Interestingly, the behavior of the World Trade Web in this new representation is strongly different from the monopartite analogue, showing highly non-trivial patterns of self-organization.

[1]  Guido Caldarelli,et al.  Bootstrapping Topological Properties and Systemic Risk of Complex Networks Using the Fitness Model , 2012, Journal of Statistical Physics.

[2]  Diego Garlaschelli,et al.  Stationarity, non-stationarity and early warning signals in economic networks , 2014, J. Complex Networks.

[3]  F. Chung,et al.  Connected Components in Random Graphs with Given Expected Degree Sequences , 2002 .

[4]  Giorgio Fagiolo,et al.  Intensive and extensive biases in economic networks: reconstructing the world trade multiplex , 2014 .

[5]  Jordi Bascompte,et al.  The architecture of mutualistic networks minimizes competition and increases biodiversity , 2009, Nature.

[6]  Dmitri V. Krioukov,et al.  Hidden Variables in Bipartite Networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Guido Caldarelli,et al.  A Network Analysis of Countries’ Export Flows: Firm Grounds for the Building Blocks of the Economy , 2011, PloS one.

[8]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[9]  Jean-Loup Guillaume,et al.  Bipartite structure of all complex networks , 2004, Inf. Process. Lett..

[10]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[11]  D. Garlaschelli,et al.  Maximum likelihood: extracting unbiased information from complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Guido Caldarelli,et al.  Measuring the Intangibles: A Metrics for the Economic Complexity of Countries and Products , 2013, PloS one.

[13]  Samuel Johnson,et al.  Factors Determining Nestedness in Complex Networks , 2013, PloS one.

[14]  J. E. Freund,et al.  Modern elementary statistics , 1953 .

[15]  Giorgio Fagiolo,et al.  Multinetwork of international trade: a commodity-specific analysis. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Jon Rokne,et al.  Encyclopedia of Social Network Analysis and Mining , 2014, Springer New York.

[17]  M. Newman,et al.  Statistical mechanics of networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  G. Fagiolo,et al.  The evolution of the world trade web: a weighted-network analysis , 2008 .

[19]  Diego Garlaschelli,et al.  Triadic motifs and dyadic self-organization in the World Trade Network , 2012, IWSOS.

[20]  Carsten F. Dormann,et al.  Introducing the bipartite Package: Analysing Ecological Networks , 2008 .

[21]  D. Garlaschelli,et al.  Reconstructing the world trade multiplex: the role of intensive and extensive biases. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Giovanni Strona,et al.  A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals , 2014, Nature Communications.

[23]  Mikko Alava,et al.  Correlations in bipartite collaboration networks , 2005, physics/0508027.

[24]  Carsten F. Dormann,et al.  Indices, Graphs and Null Models: Analyzing Bipartite Ecological Networks , 2009 .

[25]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[26]  Marián Boguñá,et al.  Correlations in weighted networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Giulio Cimini,et al.  The Scientific Competitiveness of Nations , 2014, PloS one.

[28]  M. Tumminello,et al.  Statistically Validated Networks in Bipartite Complex Systems , 2010, PloS one.

[29]  Diego Garlaschelli,et al.  Unbiased sampling of network ensembles , 2014, ArXiv.

[30]  Guido Caldarelli,et al.  A New Metrics for Countries' Fitness and Products' Complexity , 2012, Scientific Reports.

[31]  Stefano Allesina,et al.  The ghost of nestedness in ecological networks , 2013, Nature Communications.

[32]  Giorgio Fagiolo,et al.  Enhanced reconstruction of weighted networks from strengths and degrees , 2013, 1307.2104.

[33]  Frans Stokman,et al.  Encyclopedia of Social Network Analysis and Mining , 2014 .

[34]  Marián Boguñá,et al.  Topology of the world trade web. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  S. Shen-Orr,et al.  Superfamilies of Evolved and Designed Networks , 2004, Science.

[36]  Giorgio Fagiolo,et al.  Randomizing world trade. II. A weighted network analysis. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Geoffrey H. Moore,et al.  The National Bureau of Economic Research , 1950 .

[38]  G. Caldarelli,et al.  Reconstructing a credit network , 2013, Nature Physics.

[39]  Carsten F. Dormann,et al.  A method for detecting modules in quantitative bipartite networks , 2013, 1304.3218.

[40]  Albert-László Barabási,et al.  Scale-free networks , 2008, Scholarpedia.

[41]  G. Bianconi.  Entropy of network ensembles. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[43]  Daxing Xiong,et al.  q-state Potts-glass neural network based on pseudoinverse rule. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[45]  Agata Fronczak,et al.  Statistical mechanics of the international trade network , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Emanuele Pugliese,et al.  On the convergence of the Fitness-Complexity algorithm , 2014, 1410.0249.

[47]  Giorgio Fagiolo,et al.  Randomizing world trade. I. A binary network analysis. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[49]  Werner Ulrich,et al.  A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement , 2008 .

[50]  Diego Garlaschelli,et al.  Analytical maximum-likelihood method to detect patterns in real networks , 2011, 1103.0701.

[51]  César A. Hidalgo,et al.  The building blocks of economic complexity , 2009, Proceedings of the National Academy of Sciences.