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Configuring Random Graph Models with Fixed Degree Sequences

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Fosdick, Bailey K., Larremore, Daniel B., Nishimura, Joel, Ugander, Johan·2018·SIAM Review
DOI 10.1137/16m1087175
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Abstract

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 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 we 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 in-depth vignettes, analyzing three different 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.

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Metadata

Authors
Fosdick, B. K., Larremore, D. B., Nishimura, J., & Ugander, J.
Affiliations
  • Colorado State University (US)
  • Santa Fe Institute (US)
  • Stanford University (US)
ORCID
Venue
SIAM Review
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2018-01
Volume
60
Issue
2
Pages
315-355
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
DOI
10.1137/16m1087175
OpenAlex
W2484404803
Cited by
246
References
127
Citations by year
2026: 30 · 2025: 32 · 2024: 23 · 2023: 20 · 2022: 26 · 2021: 40 · 2020: 31 · 2019: 22 · 2018: 13
FWCI
13.55
Type
journal article
Language
en
Open access
Locations
  • SIAM Review (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (SES-1461495)
  • American Mathematical Society
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Graph Theory and Algorithms
  • Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Graph theory and applications
Keywords
configuration model, degree sequences, graph labeling, vertex-labeled graphs, multigraphs, self-loops, graph sampling, network analysis

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