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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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“mics, and more (see, e.g. [1, 2] for recent reviews). Random matrix theory has long been known to constitute a powerful tool to study topological properties of the graphs underlying networked systems [3, 4, 5, 1, 6]. E.g., moments of the spectral density of an adjacency matrix describing a graph, gives complete inform…”
BackgroundThe Rank of Random Binary Matrices and Distributed Storage Applications
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“rical examples, we consider that ~pis a uniform distribution with unit variance, namely, ~p(x) = 1 b [1 (x b)]; x0; (25) with b= p 3. We often consider random matrices dened on Erd}osRenyi graphs [69, 70]. For an Erd}os-Renyi graph the C ij are i.i.d. random variables that are with a probability c=(N 1) equal to one a…”
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“[7] B.”
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“Pair (5, 17) is characterized by a positive peak in H , centered in t = 0, and of width ≃ 20 msec.”
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“om graph. The theory of random graphs, initiated in 1959 by Erd¨os and R´enyi [ER60], is nowadays a well-developed and fast growing branch of discrete mathematics. The theory of random graphs [AS00], [Bol08], [JLR] offers a plethora of spectacular results and predictions playing an essential role in various engineering…”
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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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