The Impact of Projection and Backboning on Network Topologies

Bipartite networks are a well known strategy to study a variety of phenomena. The commonly used method to deal with this type of network is to project the bipartite data into a unipartite weighted graph and then using a backboning technique to extract only the meaningful edges. Despite the wide availability of different methods both for projection and backboning, we believe that there has been little attention to the effect that the combination of these two processes has on the data and on the resulting network topology. In this paper we study the effect that the possible combinations of projection and backboning techniques have on a bipartite network. We show that the 12 methods group into two clusters producing unipartite networks with very different topologies. We also show that the resulting level of network centralization is highly affected by the combination of projection and backboning applied

Transitivity and degree assortativity explained: The bipartite structure of social networks

Dynamical processes, such as the diffusion of knowledge, opinions, pathogens, "fake news", innovation, and others, are highly dependent on the structure of the social network on which they occur. However, questions on why most social networks present some particular structural features, namely high levels of transitivity and degree assortativity, when compared to other types of networks remain open. First, we argue that every one-mode network can be regarded as a projection of a bipartite network, and show that this is the case using two simple examples solved with the generating functions formalism. Second, using synthetic and empirical data, we reveal how the combination of the degree distribution of both sets of nodes of the bipartite network --- together with the presence of cycles of length four and six --- explains the observed levels of transitivity and degree assortativity in the one-mode projected network. Bipartite networks with top node degrees that display a more right-skewed distribution than the bottom nodes result in highly transitive and degree assortative projections, especially if a large number of small cycles are present in the bipartite structure.Comment: 9 pages, 6 figure

On network backbone extraction for modeling online collective behavior

Collective user behavior in social media applications often drives several important online and offline phenomena linked to the spread of opinions and information. Several studies have focused on the analysis of such phenomena using networks to model user interactions, represented by edges. However, only a fraction of edges contribute to the actual investigation. Even worse, the often large number of non-relevant edges may obfuscate the salient interactions, blurring the underlying structures and user communities that capture the collective behavior patterns driving the target phenomenon. To solve this issue, researchers have proposed several network backbone extraction techniques to obtain a reduced and representative version of the network that better explains the phenomenon of interest. Each technique has its specific assumptions and procedure to extract the backbone. However, the literature lacks a clear methodology to highlight such assumptions, discuss how they affect the choice of a method and offer validation strategies in scenarios where no ground truth exists. In this work, we fill this gap by proposing a principled methodology for comparing and selecting the most appropriate backbone extraction method given a phenomenon of interest. We characterize ten state-of-the-art techniques in terms of their assumptions, requirements, and other aspects that one must consider to apply them in practice. We present four steps to apply, evaluate and select the best method(s) to a given target phenomenon. We validate our approach using two case studies with different requirements: online discussions on Instagram and coordinated behavior in WhatsApp groups. We show that each method can produce very different backbones, underlying that the choice of an adequate method is of utmost importance to reveal valuable knowledge about the particular phenomenon under investigation

Pricing Offshore Services: Evidence from the Paradise Papers

The Paradise Papers represent one of the largest public data leaks comprising 13.4 million con_dential electronic documents. A dominant theory presented by Neal (2014) and Gri_th, Miller and O'Connell (2014) concerns the use of these offshore services in the relocation of intellectual property for the purposes of compliance, privacy and tax avoidance. Building on the work of Fernandez (2011), Billio et al. (2016) and Kou, Peng and Zhong (2018) in Spatial Arbitrage Pricing Theory (s-APT) and work by Kelly, Lustig and Van Nieuwerburgh (2013), Ahern (2013), Herskovic (2018) and Proch_azkov_a (2020) on the impacts of network centrality on _rm pricing, we use market response, discussed in O'Donovan, Wagner and Zeume (2019), to characterise the role of offshore services in securities pricing and the transmission of price risk. Following the spatial modelling selection procedure proposed in Mur and Angulo (2009), we identify Pro_t Margin and Price-to-Research as firm-characteristics describing market response over this event window. Using a social network lag explanatory model, we provide evidence for social exogenous effects, as described in Manski (1993), which may characterise the licensing or exchange of intellectual property between connected firms found in the Paradise Papers. From these findings, we hope to provide insight to policymakers on the role and impact of offshore services on securities pricing