Degree-based network models

TL;DR

This paper analyzes the sampling properties of degree-based network models, providing exact and approximate results that help understand network variability and the role of degree sequences in network structure.

Contribution

It offers a comprehensive theoretical framework for understanding the sampling variability and properties of degree-based network models, including power-law networks.

Findings

Exact sampling properties derived for degree-based models

Large-sample approximations for power-law networks

Quantification of variability within and across network populations

Abstract

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized networks is governed by properties of their degree sequences. We provide exact results and large-sample approximations for power-law networks and other more general forms. This enables us to quantify sampling variability both within and across network populations, and to characterize the limiting extremes of variation achievable through such models. Our results highlight that variation explained through expected degree structure need not be attributed to more complicated generative mechanisms.