Statistical Ensembles for Economic Networks
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Economic networks share with other social networks the fundamental property of sparsity. It is well known that the maximum entropy techniques usually employed to estimate or simulate weighted networks produce unrealistic dense topologies. At the same time, strengths should not be neglected, since they are related to core economic variables like supply and demand. To overcome this limitation, the exponential Bosonic model has been previously extended in order to obtain ensembles where the average degree and strength sequences are simultaneously fixed (conditional geometric model). In this paper a new exponential model, which is the network equivalent of Boltzmann ideal systems, is introduced and then extended to the case of joint degree-strength constraints (conditional Poisson model). Finally, the fitness of these alternative models is tested against a number of networks. While the conditional geometric model generally provides a better goodness-of-fit in terms of log-likelihoods, the conditional Poisson model could nevertheless be preferred whenever it provides a higher similarity with original data. If we are interested instead only in topological properties, the simple Bernoulli model appears to be preferable to the correlated topologies of the two more complex models.
KeywordsComplex networks Exponential networks Statistical ensembles
I would like to thank the editor and three anonymous referees for their valuable comments, which helped to markedly improve the paper. I’m also thankful to the Kyoto node of the FOC project, and in particular to Yoshi Fujiwara, for making available the Japanese bank-firm dataset. All the usual disclaimers apply. The author acknowledges the financial support from the European Community Seventh Framework Programme (FP7/2007-2013) under Socio-economic Sciences and Humanities, Grant Agreement No. 255987 (FOC-II).
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