The DOI matches its Crossref record.
Random Graphs
Abstract
In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdös and Rényi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.
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“Network analyses (Fig. 4c, see also Supplementary Notes) reveal that the mouse brain has a higher mean clustering coefficient (which gives the ratio of existing over possible connections), 0.42, than expected by a random network29,30 with identical sparseness, 0.12.”
From A mesoscale connectome of the mouse brain (2014) · cites this paper as [30]
Citations
Cited by
Sorted by citations
The Structure and Function of Complex Networks
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Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339
Opinion mining and sentiment analysis
Pang, B., & Lee, L. (2008) · Foundations and Trends® in Information Retrieval · doi:10.1561/1500000011 · Cited by 6,372
Sampling-based algorithms for optimal motion planning
Karaman, S., & Frazzoli, E. (2011) · The International Journal of Robotics Research · doi:10.1177/0278364911406761 · Cited by 5,368
“The authors are grateful to Professor MS Branicky, Professor GJ Gordon, and Professor S LaValle, as well as the anonymous reviewers, for their insightful comments on draft versions of this paper.”
BackgroundExact Matrix Completion via Convex Optimization
Candès, E. J., & Recht, B. (2009) · Foundations of Computational Mathematics · doi:10.1007/s10208-009-9045-5 · Cited by 4,972
Metadata
- Authors
- Bollobás, B.
- Affiliations
- University of Memphis (US)
- Corresponding author
- Bollobás, Béla
- ORCID
- Bollobás, Béla
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2001-08-30
- OpenAlex
- W390146837
- Cited by
- 2,639
- References
- 0
- Citations by year
- 2026: 37 · 2025: 68 · 2024: 79 · 2023: 82 · 2022: 126 · 2021: 136 · 2020: 137 · 2019: 111 · 2018: 108 · 2017: 138 · 2016: 138 · 2015: 129 · 2014: 136 · 2013: 135 · 2012: 151
- FWCI
- 6.29
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Limits and Structures in Graph Theory
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- random graphs, Erdős-Rényi random graphs, degree sequences, probabilistic combinatorics, random structures, graph enumeration
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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