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A Random Graph Model for Power Law Graphs
Abstract
We propose a random graph model which is a special case of sparserandom graphs with given degree sequences which satisfy a power law. This model involves only a small number of paramo eters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. From these parameters, various properties of the graph can be derived. For example, for certai n ranges of the parameters, we wi II compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We also discuss the threshold function, the giant component, and the evolution of random graphs in this model.
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Cites
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Cited by
Statistical physics of social dynamics
Castellano, C., Fortunato, S., & Loreto, V. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.591 · Cited by 4,119
Broido, A. D., & Clauset, A. (2019) · Nature Communications · doi:10.1038/s41467-019-08746-5 · Cited by 875
Percolation on complex networks: Theory and application
Li, M., Liu, R.-R., Lü, L., Hu, M.-B., Xu, S., & Zhang, Y.-C. (2021) · Physics Reports · doi:10.1016/j.physrep.2020.12.003 · Cited by 365
Robustness and Vulnerability of Scale-Free Random Graphs
Bollobás, B., & Riordan, O. (2004) · Internet Mathematics · doi:10.1080/15427951.2004.10129080 · Cited by 273
Metadata
- Authors
- Aiello, W., Chung, F., & Lu, L.
- Venue
- Experimental Mathematics
- Publisher
- Informa UK Limited
- Published
- 2001-01
- Volume
- 10
- Issue
- 1
- Pages
- 53-66
- ISSN
- 1058-6458 (ISSN-L)
- 1944-950X
- OpenAlex
- W2067247412
- Cited by
- 405
- References
- 1
- FWCI
- 7.43
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
