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A critical point for random graphs with a given degree sequence
Abstract
Given a sequence of nonnegative real numbers λ 0, λ 1… which sum to 1, we consider random graphs having approximately λ i n vertices of degree i. Essentially, we show that if Σ i(i ‐ 2)λ i > 0, then such graphs almost surely have a giant component, while if Σ i(i ‐2)λ. < 0, then almost surely all components in such graphs are small. We can apply these results to G n,p,G n.M, and other well‐known models of random graphs. There are also applications related to the chromatic number of sparse random graphs.
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Citations
Cited by
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Metadata
- Authors
- Molloy, M., & Reed, B.
- Venue
- Random Structures & Algorithms
- Publisher
- Wiley
- Published
- 1995-03
- Volume
- 6
- Issue
- 2-3
- Pages
- 161-180
- ISSN
- 1042-9832 (ISSN-L)
- 1098-2418
- OpenAlex
- W2044881936
- Cited by
- 2,351
- References
- 0
- FWCI
- 3.29
- Type
- journal article
- Language
- en
- Open access
- closed
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- Molloy, M., & Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures & Algorithms. https://doi.org/10.1002/rsa.3240060204
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