configuring random graph models with fixed degree sequences

• DOI: 10.48550/arxiv.1608.00607
• Publication Date: 2018-01-01
• Authors: Daniel B. Larremore; Bailey K. Fosdick; Joel Nishimura; Johan Ugander
• Keywords: 0301 basic medicine; Social and Information Networks (cs.SI); FOS: Computer and information sciences; Physics - Physics and Society; FOS: Physical sciences; Computer Science - Social and Information Networks; Physics and Society (physics.soc-ph); Quantitative Biology - Quantitative Methods; 01 natural sciences; Methodology (stat.ME); 03 medical and health sciences; Physics - Data Analysis, Statistics and Probability; FOS: Biological sciences; 0103 physical sciences; Statistics - Methodology; Data Analysis, Statistics and Probability (physics.data-an); Quantitative Methods (q-bio.QM)

To appear in SIAM Review, June 2018. Code available at github.com/joelnish/double-edge-swap-mcmc. v3 fixed minor typos<br/>Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal networks. The most popular family of random graph null models, called configuration models, are defined as uniform distributions over a space of graphs with a fixed degree sequence. Commonly, properties of an empirical network are compared to properties of an ensemble of graphs from a configuration model in order to quantify whether empirical network properties are meaningful or whether they are instead a common consequence of the particular degree sequence. In this work we study the subtle but important decisions underlying the specification of a configuration model, and investigate the role these choices play in graph sampling procedures and a suite of applications. We place particular emphasis on the importance of specifying the appropriate graph labeling (stub-labeled or vertex-labeled) under which to consider a null model, a choice that closely connects the study of random graphs to the study of random contingency tables. We show that the choice of graph labeling is inconsequential for studies of simple graphs, but can have a significant impact on analyses of multigraphs or graphs with self-loops. The importance of these choices is demonstrated through a series of three vignettes, analyzing network datasets under many different configuration models and observing substantial differences in study conclusions under different models. We argue that in each case, only one of the possible configuration models is appropriate. While our work focuses on undirected static networks, it aims to guide the study of directed networks, dynamic networks, and all other network contexts that are suitably studied through the lens of random graph null models.<br/>