Eur. Phys. J. Special Topics 212, 115–120 (2012) © EDP Sciences, Springer-Verlag 2012 DOI: 10.1140/epjst/e2012-01657-4 T HE EUROPEAN P HYSICAL JOURNAL SPECIAL TOPICS Regular Article Competitors’ communities and taxonomy of products according to export fluxes M. Cristelli 1,3 , A. Tacchella 1,2 , A. Gabrielli 2,4 , L. Pietronero 2 A. Scala 3,4 , and G. Caldarelli 5,3,4 1 “Sapienza”, Universit` a di Roma, Dip. Fisica, P.le A. Moro 2, 00185 Roma, Italy 2 ISC-CNR, Via dei Taurini 19, 00185 Roma, Italy 3 ISC-CNR, Dip. Fisica“Sapienza”, Universit` a di Roma, P.le A. Moro 2, 00185 Roma, Italy 4 London Institute for Mathematical Sciences, South Street 35a, Mayfair London, UK 5 IMT, Institute for Advanced Studies, Piazza S. Ponziano, 6, 55100 Lucca, Italy Received 31 May 2012 / Received in final form 23 July 2012 Published online 17 September 2012 Abstract. In this paper we use Complex Network Theory to quantita- tively characterize and synthetically describe the complexity of trade between nations. In particular, we focus our attention on export fluxes. Starting from the bipartite countries-products network defined by ex- port fluxes, we define two complementary graphs projecting the origi- nal network on countries and products respectively. We define, in both cases, a distance matrix amongst countries and products. Specifically, two countries are similar if they export similar products. This relation- ship can be quantified by building the Minimum Spanning Tree and the Minimum Spanning Forest from the distance matrices for products and countries. Through this simple and scalable method we are also able to carry out a community analysis. It is not gone unnoticed that in this way we can produce an effective categorization for products providing several advantages with respect to traditional classifications of COM- TRADE [1]. Finally, the forests of countries allows for the detection of competitors’ community and for the analysis of the evolution of these communities. 1 Introduction In the last two decades networks have become one of the main mathematical tools for the description of complex systems. In fact the graph theory permits for quantitative analysis, synthetic description, extraction of information and powerful visualization of a wide range of problems belonging to fields ranging from biological to social systems [2–4]. In this paper we show how the framework of networks can provide effective methods to address the problem of economic complexity. This paper is in the spirit of a recently economical theory proposed in [5, 6]. Au- thors of such papers propose to interpret the trade fluxes (in the form of a bipartite countries-products network) as the projection of a tripartite network where the in- termediate level, linking countries to products, is the key level where the information about the complexity of the productive system of a country is stored. In other words