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      Randomizing bipartite networks: the case of the World Trade Web

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          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.

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          Most cited references15

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          Assortative mixing in networks

          M. Newman (2002)
          A network is said to show assortative mixing if the nodes in the network that have many connections tend to be connected to other nodes with many connections. We define a measure of assortative mixing for networks and use it to show that social networks are often assortatively mixed, but that technological and biological networks tend to be disassortative. We propose a model of an assortative network, which we study both analytically and numerically. Within the framework of this model we find that assortative networks tend to percolate more easily than their disassortative counterparts and that they are also more robust to vertex removal.
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            The architecture of mutualistic networks minimizes competition and increases biodiversity.

            The main theories of biodiversity either neglect species interactions or assume that species interact randomly with each other. However, recent empirical work has revealed that ecological networks are highly structured, and the lack of a theory that takes into account the structure of interactions precludes further assessment of the implications of such network patterns for biodiversity. Here we use a combination of analytical and empirical approaches to quantify the influence of network architecture on the number of coexisting species. As a case study we consider mutualistic networks between plants and their animal pollinators or seed dispersers. These networks have been found to be highly nested, with the more specialist species interacting only with proper subsets of the species that interact with the more generalist. We show that nestedness reduces effective interspecific competition and enhances the number of coexisting species. Furthermore, we show that a nested network will naturally emerge if new species are more likely to enter the community where they have minimal competitive load. Nested networks seem to occur in many biological and social contexts, suggesting that our results are relevant in a wide range of fields.
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              Superfamilies of evolved and designed networks.

              Complex biological, technological, and sociological networks can be of very different sizes and connectivities, making it difficult to compare their structures. Here we present an approach to systematically study similarity in the local structure of networks, based on the significance profile (SP) of small subgraphs in the network compared to randomized networks. We find several superfamilies of previously unrelated networks with very similar SPs. One superfamily, including transcription networks of microorganisms, represents "rate-limited" information-processing networks strongly constrained by the response time of their components. A distinct superfamily includes protein signaling, developmental genetic networks, and neuronal wiring. Additional superfamilies include power grids, protein-structure networks and geometric networks, World Wide Web links and social networks, and word-adjacency networks from different languages.
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                Author and article information

                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group
                2045-2322
                01 June 2015
                2015
                : 5
                : 10595
                Affiliations
                [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)
                Author notes
                Article
                srep10595
                10.1038/srep10595
                4450581
                26029820
                8d30cb1f-64f7-4083-a849-2503c414d47e
                Copyright © 2015, Macmillan Publishers Limited

                This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

                History
                : 14 January 2015
                : 20 April 2015
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