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

Alexander P. Kartun-Giles, Dmitri Krioukov, James P. Gleeson, Yamir Moreno and Ginestra Bianconi
Entropy
2018, 20(4), 257
April 7, 2018

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.