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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The CFG model is mathematically equivalent to the Maslov-Sneppen edge-swapping null model.
“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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Self-citation
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What are higher-order networks?
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The use of multilayer network analysis in animal behaviour
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Network statistics of the whole-brain connectome of Drosophila
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Multiscale mixing patterns in networks
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Reconstructing and Stress Testing Credit Networks
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Modeling Memory Effects in Activity-Driven Networks
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Nonlinearity + Networks: A 2020 Vision
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Community detection in bipartite networks with stochastic block models
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Self-citationHipsters on networks: How a minority group of individuals can lead to an antiestablishment majority
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Relating Modularity Maximization and Stochastic Block Models in Multilayer Networks
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Modularity and Dynamics on Complex Networks
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Randomizing Hypergraphs Preserving Degree Correlation and Local Clustering
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Introduction to correlation networks: Interdisciplinary approaches beyond thresholding
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Network constraints on the mixing patterns of binary node metadata
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Generating Simple Directed Social Network Graphs for Information Spreading
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Localization and Universality of Eigenvectors in Directed Random Graphs
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A Laplacian approach to stubborn agents and their role in opinion formation on influence networks
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Percolation and the Effective Structure of Complex Networks
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The Atlas for the Aspiring Network ScientistPreprint
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Toward Principles of Brain Network Organization and Function
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Multilayer network analyses as a toolkit for measuring social structure
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Birds of a Feather Flock Together Online: Digital Inequality in Social Media Repertoires
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Separating Polarization from Noise: Comparison and Normalization of Structural Polarization Measures
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Synergistic effects in threshold models on networks
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Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks
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Random graphs with arbitrary clustering and their applications
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Gillespie Algorithms for Stochastic Multiagent Dynamics in Populations and Networks
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Message-Passing Methods for Complex Contagions
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Configuration models as an urn problem
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Complex contagions with timers
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Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
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The HyperKron Graph Model for Higher-Order Features
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Measuring directed triadic closure with closure coefficients
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Self-citationMeasuring directed triadic closure with closure coefficients
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Self-citationGraph Theory Approach to Detect Examinees Involved in Test Collusion
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Mean-field approach to evolving spatial networks, with an application to osteocyte network formation
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Latent Space Modeling of Hypergraph Data
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Measuring Quadrangle Formation in Complex Networks
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Multiplex Network Regression: How do relations drive interactions?Preprint
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Bursts of communication increase opinion diversity in the temporal Deffuant model
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Distributed network flows generate localized category selectivity in human visual cortex
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Random Graphs with Prescribed K-Core Sequences: A New Null Model for Network Analysis
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A guide to choosing and implementing reference models for social network analysis
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Self-citationA generalized hypothesis test for community structure in networks
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Systematic assessment of the quality of fit of the stochastic block model for empirical networks
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Breakup of Directed Multipartite Networks
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Predicting the diversity of early epidemic spread on networks
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Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences
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Towards quantifying the communication aspect of resilience in disaster-prone communities
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Duality between predictability and reconstructability in complex systems
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Latent Poisson models for networks with heterogeneous density
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Residual2Vec: Debiasing graph embedding with random graphsPreprint
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Generating connected random graphs
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Assessment of model fit via network comparison methods based on subgraph counts
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Concurrency and reachability in treelike temporal networks
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Inference of edge correlations in multilayer networks
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Flow-Based Algorithms for Improving Clusters: A Unifying Framework, Software, and Performance
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- 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 · 2017: 9
- 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 › Computer Vision and Pattern Recognition › Graph Theory and Algorithms
- Physical Sciences › Mathematics › Geometry and Topology › 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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