arXiv subjects

Tiziano Squartini

Publications and source records attributed to Tiziano Squartini.

80 records · Page 5Linked to original sources

arXiv2013

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

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.

q-fin.GN↗

arXiv2012

The role of distances in the World Trade Web

In the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. However, it has been recently shown that gravity models fail to reproduce the binary topology of the World Trade Web. In this paper a different approach is presented: the formalism of exponential random graphs is used and the distances are treated as constraints, to be imposed on a previously chosen ensemble of graphs. Then, the information encoded in the geographical distances is used to explain the binary structure of the World Trade Web, by testing it on the degree-degree correlations and the reciprocity structure. This leads to the definition of a novel null model that combines spatial and non-spatial effects. The effectiveness of spatial constraints is compared to that of nonspatial ones by means of the Akaike Information Criterion and the Bayesian Information Criterion. Even if it is commonly believed that the World Trade Web is strongly dependent on the distances, what emerges from our analysis is that distances do not play a crucial role in shaping the World Trade Web binary structure and that the information encoded into the reciprocity is far more useful in explaining the observed patterns.

physics.soc-ph↗

arXiv2012

Algebraic characterization of binary graphs

One of the fundamental concepts in the statistical mechanics field is that of ensemble. Ensembles of graphs are collections of graphs, defined according to certain rules. The two most used ensembles in network theory are the microcanonical and the grandcanonical (whose definitions mimick the classical ones, originally proposed by Boltzmann and Gibbs), even if the latter is far more used than the former to carry on the analytical calculations. For binary (undirected or directed) networks, the grandcanonical ensemble is defined by considering all the graphs with the same number of vertices and a variable number of links, ranging from 0 to the maximum: N(N-1)/2 for binary, undirected graphs and N(N-1) for binary, directed graphs. Even if it is commonly used almost exclusively as a tool to calculate the average of some topological quantity of interest, its structure is so rich to deserve an analysis on its own. In this paper a logic-algebraic characterization of the grandcanonical ensemble of binary graphs is provided.

physics.data-an↗

arXiv2012

Null Models of Economic Networks: The Case of the World Trade Web

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.

physics.data-an↗

arXiv2012

Triadic motifs and dyadic self-organization in the World Trade Network

In self-organizing networks, topology and dynamics coevolve in a continuous feedback, without exogenous driving. The World Trade Network (WTN) is one of the few empirically well documented examples of self-organizing networks: its topology strongly depends on the GDP of world countries, which in turn depends on the structure of trade. Therefore, understanding which are the key topological properties of the WTN that deviate from randomness provides direct empirical information about the structural effects of self-organization. Here, using an analytical pattern-detection method that we have recently proposed, we study the occurrence of triadic "motifs" (subgraphs of three vertices) in the WTN between 1950 and 2000. We find that, unlike other properties, motifs are not explained by only the in- and out-degree sequences. By contrast, they are completely explained if also the numbers of reciprocal edges are taken into account. This implies that the self-organization process underlying the evolution of the WTN is almost completely encoded into the dyadic structure, which strongly depends on reciprocity.

physics.soc-ph↗

arXiv2011

Randomizing world trade. I. A binary network analysis

The international trade network (ITN) has received renewed multidisciplinary interest due to recent advances in network theory. However, it is still unclear whether a network approach conveys additional, nontrivial information with respect to traditional international-economics analyses that describe world trade only in terms of local (first-order) properties. In this and in a companion paper, we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher-order patterns of the ITN in all its possible representations (binary/weighted, directed/undirected, aggregated/disaggregated by commodity) and across several years. Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative. Our results imply that explaining the observed degree sequence of the ITN, which has not received particular attention in economic theory, should instead become one the main focuses of models of trade.

physics.soc-ph↗

arXiv2011

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.

physics.soc-ph↗

arXiv2011

Analytical maximum-likelihood method to detect patterns in real networks

In order to detect patterns in real networks, randomized graph ensembles that preserve only part of the topology of an observed network are systematically used as fundamental null models. However, their generation is still problematic. The existing approaches are either computationally demanding and beyond analytic control, or analytically accessible but highly approximate. Here we propose a solution to this long-standing problem by introducing an exact and fast method that allows to obtain expectation values and standard deviations of any topological property analytically, for any binary, weighted, directed or undirected network. Remarkably, the time required to obtain the expectation value of any property is as short as that required to compute the same property on the single original network. Our method reveals that the null behavior of various correlation properties is different from what previously believed, and highly sensitive to the particular network considered. Moreover, our approach shows that important structural properties (such as the modularity used in community detection problems) are currently based on incorrect expressions, and provides the exact quantities that should replace them.

physics.data-an↗