Bootstrapping topology and systemic risk of complex network using the fitness model

In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, that display unconventional features on heterogeneous networks. At the same time, thanks to their deep connection with information theory, statistical physics and...

We consider the problem of risk diversification in complex networks. Nodes represent e.g. financial actors, whereas weighted links represent e.g. financial obligations (credits/debts). Each node has a risk to fail because of losses resulting from defaulting neighbors, which may lead to large failure cascades. Classical risk diversification strategies usually neglect network effects and therefore suggest that risk can be reduced if possible losses (i.e., exposures) are split a...

Network models are applied in numerous domains where data can be represented as a system of interactions among pairs of actors. While both statistical and mechanistic network models are increasingly capable of capturing various dependencies amongst these actors, these dependencies imply the lack of independence. This poses statistical challenges for analyzing such data, especially when there is only a single observed network, and often leads to intractable likelihoods regardl...

Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. In this paper we demonstrate that error tolerance is not shared by all redundant systems, but it is ...

Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in empirical network science is how to make the best possible estimates of network structure given such unreliable data. In this paper we describe a fully Bayesian method for reconstructing networks from observational data in any format, even when th...

The structure of many financial networks is protected by privacy and has to be inferred from aggregate observables. Here we consider one of the most successful network reconstruction methods, producing random graphs with desired link density and where the observed constraints (related to the market size of each node) are replicated as averages over the graph ensemble, but not in individual realizations. We show that there is a minimum critical link density below which the met...

To capture the systemic complexity of international financial systems, network data is an important prerequisite. However, dyadic data is often not available, raising the need for methods that allow for reconstructing networks based on limited information. In this paper, we are reviewing different methods that are designed for the estimation of matrices from their marginals and potentially exogenous information. This includes a general discussion of the available methodology ...

Complex networks underlie an enormous variety of social, biological, physical, and virtual systems. A profound complication for the science of complex networks is that in most cases, observing all nodes and all network interactions is impossible. Previous work addressing the impacts of partial network data is surprisingly limited, focuses primarily on missing nodes, and suggests that network statistics derived from subsampled data are not suitable estimators for the same netw...

Due to the increasingly complex and interconnected nature of global supply chain networks (SCNs), a recent strand of research has applied network science methods to model SCN growth and subsequently analyse various topological features, such as robustness. This paper provides: (1) a comprehensive review of the methodologies adopted in literature for modelling the topology and robustness of SCNs; (2) a summary of topological features of the real world SCNs, as reported in vari...

This work introduces a method for fitting to the degree distributions of complex network datasets, such that the most appropriate distribution from a set of candidate distributions is chosen while maximizing the portion of the distribution to which the model is fit. Current methods for fitting to degree distributions in the literature are inconsistent and often assume a priori what distribution the data are drawn from. Much focus is given to fitting to the tail of the distrib...