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A random graph model for massive graphs
Abstract
We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model. 1 Introduction Is the World Wide Web completely connected? If not, how big is the largest component, the second largest component, etc.? Anyone who has "surfed" the Web for any length of time will come away ...
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Cites
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Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
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The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
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Inferring friendship network structure by using mobile phone data
Eagle, N., Pentland, A. (., & Lazer, D. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0900282106 · Cited by 1,856
A Brief History of Generative Models for Power Law and Lognormal Distributions
Mitzenmacher, M. (2004) · Internet Mathematics · doi:10.1080/15427951.2004.10129088 · Cited by 1,188
Broido, A. D., & Clauset, A. (2019) · Nature Communications · doi:10.1038/s41467-019-08746-5 · Cited by 875
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Using PageRank to Characterize Web Structure
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Algorithmic Challenges in Web Search Engines
Henzinger, M. R. (2004) · Internet Mathematics · doi:10.1080/15427951.2004.10129079 · Cited by 81
A Complex Network Approach to Urban Growth
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Metadata
- Authors
- Aiello, W., Chung, F., & Lu, L.
- Venue
- Proceedings of the thirty-second annual ACM symposium on Theory of computing
- Publisher
- ACM
- Published
- 2000-05
- Pages
- 171-180
- OpenAlex
- W2097147952
- Cited by
- 917
- References
- 1
- FWCI
- 116.75
- Type
- conference paper
- Language
- en
- Open access
- closed
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