# Sparse power-law network model for reliable statistical predictions based on sampled data

## TL;DR

This paper introduces a new sparse power-law network model with hidden variables that is projective and suitable for reliable predictions from sampled data, addressing key challenges in network science.

## Contribution

It proposes a novel network process that generates sparse power-law networks with projectivity, bridging the gap between sparseness and statistical properties like exchangeability.

## Key findings

- Model generates realistic sparse power-law networks
- Close relation to exchangeable networks via information theory
- Effective as a null model on real data

## 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.