Analytical maximum-likelihood method to detect patterns in real networks

Squartini, Tiziano; Garlaschelli, Diego

doi:10.1088/1367-2630/13/8/083001

Cited by 246 publications

(606 citation statements)

References 48 publications

(136 reference statements)

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“…For example, sequential algorithms based on the properties of graphical sequences were proposed for undirected networks [9,10] and directed networks [11]. Another example is a grand-canonical model in [12] that generates a graph with given average degrees using a maximum-entropy method. However, to the best of our knowledge, none of these methods has an efficient implementation.…”

Section: Introductionmentioning

confidence: 99%

Phase transitions for scaling of structural correlations in directed networks

Hoorn

Litvak

2015

Phys. Rev. E

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Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks. Most models to date, however, show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed erased configuration model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cutoff of the network while another region has scaling similar to the structural cutoff for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to assess statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed erased configuration model.

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Section: Introductionmentioning

confidence: 99%

Phase transitions for scaling of structural correlations in directed networks

Hoorn

Litvak

2015

Phys. Rev. E

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“…This can be done analytically, by means of the probabilities appearing in eq. (1.8) [28]. The effectiveness of the degree sequence in reproducing other topological properties of the ITN is shown in fig.…”

Section: Fermi-dirac Statisticsmentioning

confidence: 98%

“…The resulting model is known as the Configuration Model, and is defined as a maximum-entropy ensemble of graphs with given degree sequence [26,28]. The degree sequence, which is the constraint defining the model, is nothing but the ordered vector k of degrees of all vertices (where the ith component k i is the degree of vertex i).…”

Section: Fermi-dirac Statisticsmentioning

confidence: 99%

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Jan Tinbergen’s Legacy for Economic Networks: From the Gravity Model to Quantum Statistics

Squartini

Garlaschelli

2014

New Economic Windows

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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.

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“…We expect, for example, the Netherlands to trade abundantly with Germany not just because of their geographic proximity, but because Germany is a hub in the European trading network. Therefore, to carve out the purely spatial information found in trading relationships, we need to disentangle spatial and non-spatial (topological effects) using a null model based on exponential random graph theory and maximum entropy graph ensembles [49]. A maximum entropy graph ensemble is, in essence, a sample of randomized networks that conserve some desired properties similar to the network under investigation, say the in and out degree sequence (or in and out strength sequence for weighted networks).…”

Section: Modelling Rebound Effect With Network Theorymentioning

confidence: 99%

The Prism of Elasticity in Rebound Effect Modelling: An Insight from the Freight Transport Sector

Ruzzenenti

2018

Sustainability

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Abstract:If the rebound effect is to be considered a major obstacle to sustainable freight transport, then action and timely policy must be made in advance. This, however, requires a theoretical understanding of the nature of the rebound effect and an empirical grasp of its underlying mechanism. Elasticity is the centrepiece of current models on the rebound effect (or Jevons paradox). Although elasticity is a metric of indisputable usefulness for empirical purposes, it may be misleading when applied to the complex rebound effect. Drawing on the parallel case of the 'distance puzzle' in international economics, it will be shown how elasticity can be misinterpreted or how it can misdirect an investigation of the phenomenon by following a predetermined mindset. This particular bias is shown to widen in the long term and evolving systems in which the elasticity metric continues to output a constant number, eliciting a persistent effect. Drawing on previous research, an alternative approach to studying the rebound effect based on complex network theory and statistical mechanics of networks will be described. It will be shown how the interplay between spatial and non-spatial effects in freight transport networks can inform us about the evolution of the effect of distances on trade relationships, upon which a new metric for the rebound effect can be built.

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Analytical maximum-likelihood method to detect patterns in real networks

Cited by 246 publications

References 48 publications

Phase transitions for scaling of structural correlations in directed networks

Phase transitions for scaling of structural correlations in directed networks

Jan Tinbergen’s Legacy for Economic Networks: From the Gravity Model to Quantum Statistics

The Prism of Elasticity in Rebound Effect Modelling: An Insight from the Freight Transport Sector

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