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Configuring Random Graph Models with Fixed Degree Sequences
Open accessAbstract
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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“With these conditions, this CFG model is mathematically equivalent to the Maslov–Sneppen edge-swapping null model66–68.”
From Network statistics of the whole-brain connectome of Drosophila (2024) · cites this paper as [68]
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Kojaku, S., Yoon, J., Constantino, I., & Ahn, Y. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.07654 · Cited by 9
Weir, W. H., Mucha, P. J., & Kim, W. Y. (2022) · Cell Reports Medicine · doi:10.1016/j.xcrm.2022.100602 · Cited by 9
Generating connected random graphs
Gray, C., Mitchell, L., & Roughan, M. (2019) · Journal of Complex Networks · doi:10.1093/comnet/cnz011 · Cited by 8
Degree correlations in graphs with clique clustering
Mann, P., Smith, V. A., Mitchell, J. B. O., & Dobson, S. (2022) · Physical review. E · doi:10.1103/physreve.105.044314 · Cited by 8
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Ospina-Forero, L., Deane, C. M., & Reinert, G. (2018) · Journal of Complex Networks · doi:10.1093/comnet/cny017 · Cited by 8
Concurrency and reachability in treelike temporal networks
Lee, E., Emmons, S., Gibson, R., Moody, J. W., & Mucha, P. J. (2019) · Physical review. E · doi:10.1103/physreve.100.062305 · Cited by 8
Inference of edge correlations in multilayer networks
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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)
- Venue
- SIAM Review
- Published
- 2018-01
- Volume
- 60
- Issue
- 2
- Pages
- 315-355
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- 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
- green
- arxiv.org
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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