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Solution of the two-star model of a network
Open accessAbstract
The p-star model or exponential random graph is among the oldest and best known of network models. Here we give an analytic solution for the particular case of the two-star model, which is one of the most fundamental of exponential random graphs. We derive expressions for a number of quantities of interest in the model and show that the degenerate region of the parameter space observed in computer simulations is a spontaneously symmetry-broken phase separated from the normal phase of the model by a conventional continuous phase transition.
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Dorogovtsev, S. N., & Mendes, J. F. F. (2003) · doi:10.1093/acprof:oso/9780198515906.001.0001 · Cited by 1,563
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Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1275 · Cited by 2,220
New Specifications for Exponential Random Graph Models
Snijders, T. A. B., Pattison, P. E., Robins, G. L., & Handcock, M. S. (2006) · Sociological Methodology · doi:10.1111/j.1467-9531.2006.00176.x · Cited by 1,445
Recent developments in exponential random graph (p*) models for social networks
Robins, G., Snijders, T., Wang, P., Handcock, M., & Pattison, P. (2007) · Social Networks · doi:10.1016/j.socnet.2006.08.003 · Cited by 832
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
Entropy measures for networks: Toward an information theory of complex topologies
Anand, K., & Bianconi, G. (2009) · Physical Review E · doi:10.1103/physreve.80.045102 · Cited by 368
Metadata
- Authors
- Park, J., & Newman, M. E. J.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2004-12-29
- Volume
- 70
- Issue
- 6
- Pages
- 066146-066146
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2019258379
- Cited by
- 164
- References
- 1
- FWCI
- 2.05
- Type
- journal article
- Language
- en
- Open access
- green
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- Park, J., & Newman, M. E. J. (2004). Solution of the two-star model of a network. Physical Review E. https://doi.org/10.1103/physreve.70.066146
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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.
