2012/11/28 by Sofia C. Olhede, Olhede, Sofia C., Patrick J. Wolfe +1 · 1 citation
Computer Science · Physics and Astronomy · #05C80 (Primary) 62G05 #60B20 (Secondary) #Advanced Graph Neural Networks #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Social and Information Networks (cs.SI) #Statistics Theory (math.ST) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1211.6537
openalex publication_date 2012/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.