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

Randomizing bipartite networks: the case of the World Trade Web