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A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees
Open accessAbstract
Random graphs with given degrees are a natural next step in complexity beyond the Erdős–Rényi model, yet the degree constraint greatly complicates simulation and estimation. We use an extension of a combinatorial characterization due to Erdős and Gallai to develop a sequential algorithm for generating a random labeled graph with a given degree sequence. The algorithm is easy to implement and allows for surprisingly efficient sequential importance sampling. The resulting probabilities are easily computed on the fly, allowing the user to reweight estimators appropriately, in contrast to some ad hoc approaches that generate graphs with the desired degrees but with completely unknown probabilities. Applications are given, including simulating an ecological network and estimating the number of graphs with a given degree sequence.
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Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Network motifs: simple building blocks of complex networks.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002) · Science · doi:10.1126/science.298.5594.824 · Cited by 7,368
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A Survey of Statistical Network Models
Goldenberg, A., Zheng, A. X., Fienberg, S. E., & Airoldi, E. M. (2010) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000005 · Cited by 819
Resisting structural re-identification in anonymized social networks
Hay, M., Miklau, G., Jensen, D., Towsley, D., & Weis, P. (2008) · Proceedings of the VLDB Endowment · doi:10.14778/1453856.1453873 · Cited by 549
The physics of financial networks
Bardoscia, M., Barucca, P., Battiston, S., Caccioli, F., Cimini, G., Garlaschelli, D., Saracco, F., Squartini, T., & Caldarelli, G. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00322-5 · Cited by 281
Configuring Random Graph Models with Fixed Degree Sequences
Fosdick, B. K., Larremore, D. B., Nishimura, J., & Ugander, J. (2018) · SIAM Review · doi:10.1137/16m1087175 · Cited by 246
Metadata
- Authors
- Blitzstein, J., & Diaconis, P.
- Venue
- Internet Mathematics
- Publisher
- Internet Mathematics
- Published
- 2011-03-09
- Volume
- 6
- Issue
- 4
- Pages
- 489-522
- ISSN
- 1542-7951 (ISSN-L)
- 1944-9488
- OpenAlex
- W1978479505
- Cited by
- 291
- References
- 2
- FWCI
- 18.17
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
