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.

Revealing in-block nestedness: Detection and benchmarking

“…Nestedness has imposed itself as a landmark feature in mutualistic interactions, with an emphasis in natural ecosystems, triggering a large amount of research spanning fieldwork [2], modeling [4], and simulation [5]. Beyond natural systems, nestedness emerges as well in social, technical, and economic systems, e.g., industrial relationships [4,6,7], international trade [8], information ecosystems [9], anthropology [10], and knowledge production [11]. In socioeconomic systems, the epitome of this property in unipartite networks, the emergence of nestedness is originated in agents attempting to maximize their own centrality [12][13][14].…”

Assessing Systemic Risk Due to Fire Sales Spillover Through Maximum Entropy Network Reconstruction

“…Although sizes and capitalizations are the only information required to construct the ensemble, we show that it does a very good job in predicting systemic risk metrics, not only at aggregate level, but also for each bank. The performances of this newly proposed approach are shown to outperform those obtained with standard maximum entropy approaches (Saracco et al, 2015), i.e. the bipartite extensions of the models proposed by Mastrandrea et al (2014) for unipartite networks.…”

“…Since other specifications of maximum entropy are quite popular in the literature of network reconstruction, only for comparison purposes we take into considerations two other ensembles, mainly inspired by the paper by Mastrandrea et al (2014) and Saracco et al (2015). Each of them is characterized by different constraints imposed on the maximization of the Shannon's entropy.…”

Measuring Nestedness: A comparative study of the performance of different metrics

“…These two requirements warrant that the resulting ensemble is maximally disordered while enforcing the average degree sequences in the ensemble to be equal to the degree sequences of the corresponding real network, which in turn are the most probable degree sequences for each guild. This randomizing framework was first developed by Squartini and Garlaschelli [30], then extended to bipartite networks by Saracco et al [41]. We also applied it to the study of the emergence of nestedness in ecological networks in [18], where the interested reader will find a more detailed description of the null model.…”