Showing papers by "Tiziano Squartini published in 2013"

Early-warning signals of topological collapse in interbank networks

Abstract: The financial crisis clearly illustrated the importance of characterizing the level of ‘systemic’ risk associated with an entire credit network, rather than with single institutions. However, the interplay between financial distress and topological changes is still poorly understood. Here we analyze the quarterly interbank exposures among Dutch banks over the period 1998–2008, ending with the crisis. After controlling for the link density, many topological properties display an abrupt change in 2008, providing a clear – but unpredictable – signature of the crisis. By contrast, if the heterogeneity of banks' connectivity is controlled for, the same properties show a gradual transition to the crisis, starting in 2005 and preceded by an even earlier period during which anomalous debt loops could have led to the underestimation of counter-party risk. These early-warning signals are undetectable if the network is reconstructed from partial bank-specific data, as routinely done. We discuss important implications for bank regulatory policies.

Reciprocity of weighted networks

Abstract: In directed networks, reciprocal links have dramatic effects on dynamical processes, network growth, and higher-order structures such as motifs and communities. While the reciprocity of binary networks has been extensively studied, that of weighted networks is still poorly understood, implying an ever-increasing gap between the availability of weighted network data and our understanding of their dyadic properties. Here we introduce a general approach to the reciprocity of weighted networks, and define quantities and null models that consistently capture empirical reciprocity patterns at different structural levels. We show that, counter-intuitively, previous reciprocity measures based on the similarity of mutual weights are uninformative. By contrast, our measures allow to consistently classify different weighted networks according to their reciprocity, track the evolution of a network's reciprocity over time, identify patterns at the level of dyads and vertices, and distinguish the effects of flux (im)balances or other (a)symmetries from a true tendency towards (anti-)reciprocation.

Null models of economic networks: the case of the world trade web

Abstract: In all empirical-network studies, the observed properties of economic networks are informative only if compared with a well-defined null model that can quantitatively predict the behavior of such properties in constrained graphs. However, predictions of the available null-model methods can be derived analytically only under assumptions (e.g., sparseness of the network) that are unrealistic for most economic networks like the world trade web (WTW). In this paper we study the evolution of the WTW using a recently-proposed family of null network models. The method allows to analytically obtain the expected value of any network statistic across the ensemble of networks that preserve on average some local properties, and are otherwise fully random. We compare expected and observed properties of the WTW in the period 1950–2000, when either the expected number of trade partners or total country trade is kept fixed and equal to observed quantities. We show that, in the binary WTW, node-degree sequences are sufficient to explain higher-order network properties such as disassortativity and clustering-degree correlation, especially in the last part of the sample. Conversely, in the weighted WTW, the observed sequence of total country imports and exports are not sufficient to predict higher-order patterns of the WTW. We discuss some important implications of these findings for international-trade models.

Enhanced network reconstruction from irreducible local information

Abstract: Network topology plays a key role in many phenomena, from the spreading of diseases to that of nancial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case is when there is only local (node-specic) information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naive approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths, and as `fundamental' as the latter. This implies that the reconstruction of weighted networks would be signicantly enhanced by the specication of both quantities, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world applications and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously conrm that the binary information is irreducible to the weighted one. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns.

Enhanced network reconstruction from irreducible local information

Abstract: Network topology plays a key role in many phenomena, from the spreading of diseases to that of nancial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case is when there is only local (node-specic) information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naive approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths, and as `fundamental' as the latter. This implies that the reconstruction of weighted networks would be signicantly enhanced by the specication of both quantities, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world applications and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously conrm that the binary information is irreducible to the weighted one. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns.

Economic Networks In and Out of Equilibrium

Abstract: Economic and financial networks play a crucial role in various important processes, including economic integration, globalization, and financial crises. Of particular interest is understanding whether the temporal evolution of a real economic network is in a (quasi-)stationary equilibrium, i.e. characterized by smooth structural changes rather than abrupt transitions. Smooth changes in quasi-equilibrium networks can be generally controlled for, and largely predicted, while this is generally not possible for abrupt transitions in non-stationary networks. Here we study whether real economic networks are in or out of equilibrium by checking their consistency with quasi-equilibrium maximum-entropy ensembles of graphs. As illustrative examples, we consider the International Trade Network (ITN) and the Dutch Interbank Network (DIN). We show that, despite the globalization process, the ITN is an almost perfect example of quasi-equilibrium network, while the DIN is clearly an out-of-equilibrium network undergoing major structural changes and displaying non-stationary dynamics. Among the out-of-equilibrium properties of the DIN, we find striking early-warning signals of the interbank crisis of 2008.

Enhanced reconstruction of weighted networks from strengths and degrees

Abstract: Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value However, for weighted networks the problem is much more complicated While the naive approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns

Jan Tinbergen's legacy for economic networks: from the gravity model to quantum statistics

Abstract: Jan Tinbergen, the first recipient of the Nobel Memorial Prize in Economics in 1969, obtained his PhD in physics at the University of Leiden under the supervision of Paul Ehrenfest in 1929. Among many achievements as an economist after his training as a physicist, Tinbergen proposed the so-called Gravity Model of international trade. The model predicts that the intensity of trade between two countries is described by a formula similar to Newton's law of gravitation, where mass is replaced by Gross Domestic Product. Since Tinbergen's proposal, the Gravity Model has become the standard model of non-zero trade flows in macroeconomics. However, its intrinsic limitation is the prediction of a completely connected network, which fails to explain the observed intricate topology of international trade. Recent network models overcome this limitation by describing the real network as a member of a maximum-entropy statistical ensemble. The resulting expressions are formally analogous to quantum statistics: the international trade network is found to closely follow the Fermi-Dirac statistics in its purely binary topology, and the recently proposed mixed Bose-Fermi statistics in its full (binary plus weighted) structure. This seemingly esoteric result is actually a simple effect of the heterogeneity of world countries, that imposes strong structural constraints on the network. Our discussion highlights similarities and differences between macroeconomics and statistical-physics approaches to economic networks.

Early-warning signals of topological collapse in interbank networks

Abstract: The financial crisis clearly illustrated the importance of characterizing the level of 'systemic' risk associated with an entire credit network, rather than with single institutions. However, the interplay between financial distress and topological changes is still poorly understood. Here we analyze the quarterly interbank exposures among Dutch banks over the period 1998-2008, ending with the crisis. After controlling for the link density, many topological properties display an abrupt change in 2008, providing a clear - but unpredictable - signature of the crisis. By contrast, if the heterogeneity of banks' connectivity is controlled for, the same properties show a gradual transition to the crisis, starting in 2005 and preceded by an even earlier period during which anomalous debt loops could have led to the underestimation of counter-party risk. These early-warning signals are undetectable if the network is reconstructed from partial bank-specific data, as routinely done. We discuss important implications for bank regulatory policies.

Economic networks in and out of equilibrium

Abstract: Economic and financial networks play a crucial role in various important processes, including economic integration, globalization, and financial crises. Of particular interest is understanding whether the temporal evolution of a real economic network is in a (quasi-)stationary equilibrium, i.e. characterized by smooth structural changes rather than abrupt transitions. Smooth changes in quasi-equilibrium networks can be generally controlled for, and largely predicted, via an appropriate rescaling of structural quantities, while this is generally not possible for abrupt transitions in non-stationary networks. Here we study whether real economic networks are in or out of equilibrium by checking their consistency with quasi-equilibrium maximum-entropy ensembles of graphs. As illustrative examples, we consider the International Trade Network (ITN) and the Dutch Interbank Network (DIN). We show that, despite the globalization process, the ITN is an almost perfect example of quasi-equilibrium network, while the DIN is clearly an out-of-equilibrium network undergoing major structural changes and displaying non-stationary dynamics. Among the out-of-equilibrium properties of the DIN, we find striking early-warning signals of the interbank crisis of 2008.