2012/01/27 by Patrick O. Perry, Perry, Patrick O., Patrick J. Wolfe +1 · 1 voice · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Graph theory and applications #Methodology (stat.ME) #Social and Information Networks (cs.SI) #Statistics Theory (math.ST) #cs.SI #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1201.5871
12 pages, 2 figures; submitted for publication
arxiv created 2012/01/27 · openalex publication_date 2012/01/27 · arxiv published 2012/01/27 · arxiv updated 2012/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The analysis of datasets taking the form of simple, undirected graphs continues to gain in importance across a variety of disciplines. Two choices of null model, the logistic-linear model and the implicit log-linear model, have come into common use for analyzing such network data, in part because each accounts for the heterogeneity of network node degrees typically observed in practice. Here we show how these both may be viewed as instances of a broader class of null models, with the property that all members of this class give rise to essentially the same likelihood-based estimates of link probabilities in sparse graph regimes. This facilitates likelihood-based computation and inference, and enables practitioners to choose the most appropriate null model from this family based on application context. Comparative model fits for a variety of network datasets demonstrate the practical implications of our results.