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The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Open accessAbstract
Given a sequence of nonnegative real numbers λ0, λ1, … that sum to 1, we consider a random graph having approximately λin vertices of degree i. In [12] the authors essentially show that if [sum ]i(i−2)λi>0 then the graph a.s. has a giant component, while if [sum ]i(i−2)λi<0 then a.s. all components in the graph are small. In this paper we analyse the size of the giant component in the former case, and the structure of the graph formed by deleting that component. We determine ε, λ′0, λ′1 … such that a.s. the giant component, C, has εn+o(n) vertices, and the structure of the graph remaining after deleting C is basically that of a random graph with n′=n−[mid ]C[mid ] vertices, and with λ′in′ of them of degree i.
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Citations
Cited by
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Castellano, C., Fortunato, S., & Loreto, V. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.591 · Cited by 4,119
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Mislove, A., Marcon, M., Gummadi, K. P., Druschel, P., & Bhattacharjee, B. (2007) · Proceedings of the 7th ACM SIGCOMM conference on Internet measurement · doi:10.1145/1298306.1298311 · Cited by 3,057
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Metadata
- Authors
- MOLLOY, M., & REED, B.
- Venue
- Combinatorics, Probability and Computing
- Publisher
- Cambridge University Press (CUP)
- Published
- 1998-09
- Volume
- 7
- Issue
- 3
- Pages
- 295-305
- ISSN
- 0963-5483 (ISSN-L)
- 1469-2163
- OpenAlex
- W2129918926
- Cited by
- 831
- References
- 0
- FWCI
- 11.21
- Type
- journal article
- Language
- en
- Open access
- bronze
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- MOLLOY, M., & REED, B. (1998). The Size of the Giant Component of a Random Graph with a Given Degree Sequence. Combinatorics, Probability and Computing. https://doi.org/10.1017/s0963548398003526
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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.
