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.

Bipartite networks are currently regarded as providing a major insight into the organization of many real-world systems, unveiling the mechanisms driving the interactions occurring between distinct groups of nodes. One of the most important issues encountered when modeling bipartite networks is devising a way to obtain a (monopartite) projection on the layer of interest, which preserves as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm to obtain statistically-validated projections of bipartite networks, according to which any two nodes sharing a statistically-significant number of neighbors are linked. Since assessing the statistical significance of nodes similarity requires a proper statistical benchmark, here we consider a set of four null models, defined within the Exponential Random Graph framework. Our algorithm outputs a matrix of link-specific p-values, from which a validated projection is straightforwardly obtainable, upon running a multiple hypothesis testing procedure. Finally, we test our method on an economic network (i.e. the countries-products World Trade Web representation) and a social network (i.e. MovieLens, collecting the users' ratings of a list of movies). In both cases non-trivial communities are detected: while projecting the World Trade Web on the countries layer reveals modules of similarly-industrialized nations, projecting it on the products layer allows communities characterized by an increasing level of complexity to be detected; in the second case, projecting MovieLens on the films layer allows clusters of movies whose affinity cannot be fully accounted for by genre similarity to be individuated.

Common asset holding by financial institutions (portfolio overlap) is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and severe losses at the systemic level. We propose a method to assess the statistical significance of the overlap between heterogeneously diversified portfolios, which we use to build a validated network of financial institutions where links indicate potential contagion channels. The method is implemented on a historical database of institutional holdings ranging from 1999 to the end of 2013, but can be applied to any bipartite network. We find that the proportion of validated links (i.e. of significant overlaps) increased steadily before the 2007–2008 financial crisis and reached a maximum when the crisis occurred. We argue that the nature of this measure implies that systemic risk from fire sales liquidation was maximal at that time. After a sharp drop in 2008, systemic risk resumed its growth in 2009, with a notable acceleration in 2013. We finally show that market trends tend to be amplified in the portfolios identified by the algorithm, such that it is possible to have an informative signal about institutions that are about to suffer (enjoy) the most significant losses (gains).

Since 2007, several contributions have tried to identify early-warning signals of the financial crisis. However, the vast majority of analyses has focused on financial systems and little theoretical work has been done on the economic counterpart. In the present paper we fill this gap and employ the theoretical tools of network theory to shed light on the response of world trade to the financial crisis of 2007 and the economic recession of 2008–2009. We have explored the evolution of the bipartite World Trade Web (WTW) across the years 1995–2010, monitoring the behavior of the system both before and after 2007. Our analysis shows early structural changes in the WTW topology: since 2003, the WTW becomes increasingly compatible with the picture of a network where correlations between countries and products are progressively lost. Moreover, the WTW structural modification can be considered as concluded in 2010, after a seemingly stationary phase of three years. We have also refined our analysis by considering specific subsets of countries and products: the most statistically significant early-warning signals are provided by the most volatile macrosectors, especially when measured on developing countries, suggesting the emerging economies as being the most sensitive ones to the global economic cycles.

1. Bipartite networks are widely used to represent a diverse range of species interactions, such as pollination, herbivory, parasitism and seed dispersal. The structure of these networks is usually characterised by calculating one or more indices that capture different aspects of network architecture. While these indices capture useful properties of networks, they are relatively insensitive to changes in network structure. Consequently, variation in ecologically-important interactions can be missed. Network motifs are a way to characterise network structure that is substantially more sensitive to changes in pairwise interactions and is gaining in popularity. However, there is no software available in R, the most popular programming language among ecologists, for conducting motif analyses in bipartite networks. Similarly, no mathematical formalisation of bipartite motifs has been developed.2. Here we introduce bmotif: a package for motif analyses of bipartite networks. Our code is primarily an r package, but we also provide matlab and Python code of the core functionality. The software is based on a mathematical framework where, for the first time, we derive formal expressions for motif frequencies and the frequencies with which species occur in different positions within motifs. This framework means that analyses with bmotif are fast, making motif methods compatible with the permutational approaches often used in network studies, such as null model analyses.3. We describe the package and demonstrate how it can be used to conduct ecological analyses, using two examples of plant-pollinator networks. We first use motifs to examine the assembly and disassembly of an Arctic plant-pollinator community and then use them to compare the roles of native and introduced plant species in an unrestored site in Mauritius.4. bmotif will enable motif analyses of a wide range of bipartite ecological networks, allowing future research to characterise these complex networks without discarding important meso-scale structural detail. K E Y W O R D Sbipartite networks, food web, matlab, motifs, pollination, Python, R, seed dispersal This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Zipf-like distributions characterize a wide set of phenomena in physics, biology, economics, and social sciences. In human activities, Zipf's law describes, for example, the frequency of appearance of words in a text or the purchase types in shopping patterns. In the latter, the uneven distribution of transaction types is bound with the temporal sequences of purchases of individual choices. In this work, we define a framework using a text compression technique on the sequences of credit card purchases to detect ubiquitous patterns of collective behavior. Clustering the consumers by their similarity in purchase sequences, we detect five consumer groups. Remarkably, post checking, individuals in each group are also similar in their age, total expenditure, gender, and the diversity of their social and mobility networks extracted from their mobile phone records. By properly deconstructing transaction data with Zipf-like distributions, this method uncovers sets of significant sequences that reveal insights on collective human behavior.

Social networks amplify inequalities by fundamental mechanisms of social tie formation such as homophily and triadic closure. These forces sharpen social segregation, which is reflected in fragmented social network structure. Geographical impediments such as distance and physical or administrative boundaries also reinforce social segregation. Yet, less is known about the joint relationships between social network structure, urban geography, and inequality. In this paper we analyze an online social network and find that the fragmentation of social networks is significantly higher in towns in which residential neighborhoods are divided by physical barriers such as rivers and railroads. Towns in which neighborhoods are relatively distant from the center of town and amenities are spatially concentrated are also more socially segregated. Using a two-stage model, we show that these urban geography features have significant relationships with income inequality via social network fragmentation. In other words, the geographic features of a place can compound economic inequalities via social networks.

221. Bipartite networks are widely-used to represent a diverse range of species interactions, such as 23 pollination, herbivory, parasitism and seed dispersal. The structure of these networks is usually 24 characterised by calculating one or more metrics that capture different aspects of network architecture. 25While these metrics capture useful properties of networks, they only consider structure at the scale of 26 the whole network (the macro-scale) or individual species (the micro-scale). 'Meso-scale' structure 27 between these scales is usually ignored, despite representing ecologically-important interactions. 28Network motifs are a framework for capturing this meso-scale structure and are gaining in popularity. 29However, there is no software available in R, the most popular programming language among 30 ecologists, for conducting motif analyses in bipartite networks. Similarly, no mathematical 31 formalisation of bipartite motifs has been developed. 32 2. Here we introduce bmotif: a package for counting motifs, and species positions within motifs, in 33 bipartite networks. Our code is primarily an R package, but we also provide MATLAB and Python code 34 of the core functionality. The software is based on a mathematical framework where, for the first time, 35we derive formal expressions for motif frequencies and the frequencies with which species occur in 36 different positions within motifs. This framework means that analyses with bmotif are fast, making 37 motif methods compatible with the permutational approaches often used in network studies, such as 38 null model analyses. 39 3. We describe the package and demonstrate how it can be used to conduct ecological analyses, using 40 two examples of plant-pollinator networks. We first use motifs to examine the assembly and 41 disassembly of an Arctic plant-pollinator community, and then use them to compare the roles of native 42 and introduced plant species in an unrestored site in Mauritius. 43 4. bmotif will enable motif analyses of a wide range of bipartite ecological networks, allowing future 44 research to characterise these complex networks without discarding important meso-scale structural 45 detail. 46 47