Maximum likelihood: Extracting unbiased information from complex networks

Garlaschelli, Diego; Loffredo, Maria I.

doi:10.1103/physreve.78.015101

Cited by 169 publications

(301 citation statements)

References 25 publications

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“…The method we use to introduce null models of the World Trade Web implements a recently proposed procedure [9], [12], developed inside the exponential random graph theoretical famework [13], [14], [15]. The method is composed by two main steps: the first one is the maximization of the Shannon entropy over a previously chosen set of graphs, G…”

Section: Null Modelsmentioning

confidence: 99%

The Role of Distances in the World Trade Web

Picciolo

Squartini

Ruzzenenti

et al. 2012

2012 Eighth International Conference on Signal Image Technology and Internet Based Systems

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Abstract-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.

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Section: Null Modelsmentioning

confidence: 99%

The Role of Distances in the World Trade Web

Picciolo

Squartini

Ruzzenenti

et al. 2012

2012 Eighth International Conference on Signal Image Technology and Internet Based Systems

Self Cite

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“…The present work deals with the challenge of introducing null models that provide exact analytical expectations for the main network observables under some given fixed constraints. This, in turn, allows one to assess whether any observed network characteristic from real data is due to the imposed constraints [16] or to the contrary, to some unexpected phenomena worth exploring.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of multiedge networks

2013

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Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

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“…The material of this appendix is original but rephrased from several other sources [17][18][19]. In general terms, an ensemble of random graphs is a collection of graphs generated with some random mechanism such that each particular graph instance A ≡ {a ij } is generated with probability P (A), where A is the adjacency matrix.…”

Section: Appendix B: Canonical Ensembles Of Maximally Random Graphsmentioning

confidence: 99%

“…The particular form chosen for the connection probability ensures that the entropy of the ensemble is maximal [17][18][19] (see also Appendix B).…”

Section: Clustering In Maximally Random Graphs With Expected Degrmentioning

confidence: 99%

Clustering of random scale-free networks

Colomer-de-Simón

Boguñá

2012

Phys. Rev. E

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We derive the finite-size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent 2 < γ < 3. Degree heterogeneity increases the presence of triangles in the network up to levels that compare to those found in many real networks even for extremely large nets. We also find that for values of γ ≈ 2, clustering is virtually size independent and, at the same time, becomes a de facto non-self-averaging topological property. This implies that a single-instance network is not representative of the ensemble even for very large network sizes.

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Maximum likelihood: Extracting unbiased information from complex networks

Cited by 169 publications

References 25 publications

The Role of Distances in the World Trade Web

The Role of Distances in the World Trade Web

Statistical mechanics of multiedge networks

Clustering of random scale-free networks

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