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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]
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“e the number of copies of a xed graph Hin G n;p. Note that E[X] = ( nv Hpe H). Since controlling the distribution of Xfor completely general graphs involves many technical diculties (see for example [11, 57]), we will restrict our attention to connected, -regular graphs H. If the expected value of Xis bounded, then Xc…”
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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
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