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Entropy 2018, 20(4), 257; https://doi.org/10.3390/e20040257

Sparse Power-Law Network Model for Reliable Statistical Predictions Based on Sampled Data

1
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
2
Departments of Physics, Mathematics, and Electrical & Computer Engineering, Northeastern University, Boston 02120, MA, USA
3
MACSI, Department of Mathematics and Statistics, University of Limerick, Limerick V94 T9PX, Ireland
4
Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50013, Spain
5
Department of Theoretical Physics, Faculty of Sciences, University of Zaragoza, Zaragoza 50013, Spain
6
Institute for Scientific Interchange (ISI Foundation), Turin 10121, Italy
7
Complexity Science Hub Vienna, Vienna 22180, Austria
*
Author to whom correspondence should be addressed.
Received: 2 March 2018 / Revised: 4 April 2018 / Accepted: 5 April 2018 / Published: 7 April 2018
(This article belongs to the Special Issue Graph and Network Entropies)
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Abstract

A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model that does not depend on the order in which nodes are sampled. Despite a large variety of non-equilibrium (growing) and equilibrium (static) sparse complex network models that are widely used in network science, how to reconcile sparseness (constant average degree) with the desired statistical properties of projectivity and exchangeability is currently an outstanding scientific problem. Here we propose a network process with hidden variables which is projective and can generate sparse power-law networks. Despite the model not being exchangeable, it can be closely related to exchangeable uncorrelated networks as indicated by its information theory characterization and its network entropy. The use of the proposed network process as a null model is here tested on real data, indicating that the model offers a promising avenue for statistical network modelling. View Full-Text
Keywords: networks models; projectivity and exchangeability; network entropy; information theory of networks networks models; projectivity and exchangeability; network entropy; information theory of networks
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Kartun-Giles, A.P.; Krioukov, D.; Gleeson, J.P.; Moreno, Y.; Bianconi, G. Sparse Power-Law Network Model for Reliable Statistical Predictions Based on Sampled Data. Entropy 2018, 20, 257.

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