title: Randomizing bipartite networks: the case of the World Trade Web.
abstract: 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.
authors.affiliation: Istituto dei Sistemi Complessi (ISC) - CNR, UoS Sapienza, Dipartimento di Fisica, Universitá "Sapienza" di Roma, P.le A. Moro 5, 00185 Roma (Italy).
authors.forename: Fabio
authors.initials: F
authors.lastname: Saracco
authors.affiliation: Istituto dei Sistemi Complessi (ISC) - CNR, UoS Sapienza, Dipartimento di Fisica, Universitá "Sapienza" di Roma, P.le A. Moro 5, 00185 Roma (Italy).
authors.forename: Riccardo
authors.initials: R
authors.lastname: Di Clemente
authors.affiliation: 1] Istituto dei Sistemi Complessi (ISC) - CNR, UoS Sapienza, Dipartimento di Fisica, Universitá "Sapienza" di Roma, P.le A. Moro 5, 00185 Roma (Italy) [2] IMT Institute for Advanced Studies, P.zza S. Ponziano 6, 55100 Lucca (Italy) [3] INFN - Unitá Roma1, Dipartimento di Fisica, Universitá "Sapienza di Roma, P.le A. Moro 5, 00185 Roma (Italy).
authors.forename: Andrea
authors.initials: A
authors.lastname: Gabrielli
authors.affiliation: Istituto dei Sistemi Complessi (ISC) - CNR, UoS Sapienza, Dipartimento di Fisica, Universitá "Sapienza" di Roma, P.le A. Moro 5, 00185 Roma (Italy).
authors.forename: Tiziano
authors.initials: T
authors.lastname: Squartini