The DOI matches its Crossref record.
Evolution of Networks
Abstract
Only recently did mankind realise that it resides in a world of networks. The Internet and World Wide Web are changing our life. Our physical existence is based on various biological networks. We have recently learned that the term network turns out to be a central notion in our time, and the consequent explosion of interest in networks is a social and cultural phenomenon. The principles of the complex organization and evolution of networks, natural and artificial, are the topic of this book, which is written by physicists and is addressed to all involved researchers and students. The aim of the text is to understand networks and the basic principles of their structural organization and evolution. The ideas are presented in a clear and a pedagogical way, with minimal mathematics, so even students without a deep knowledge of mathematics and statistical physics will be able to rely on this as a reference. Special attention is given to real networks, both natural and artifical. Collected empirical data and numerous real applications of existing theories are discussed in detail, as well as the topical problems of communication networks. Available in OSO: http://www.oxfordscholarship.com/oso/public/content/physics/9780198515906/toc.html
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In the citing paper
“Using the master equation approach [50-52] we show that depending on the dimensions d and δ , and on the flavor s , the generalized degrees k d,δ can follow either binomial or exponential or power-law distributions.”
From Network geometry with flavor: From complexity to quantum geometry (2016) · cites this paper as [50]
In the citing paper
“For deriving our results at β = 0 we use the master equation approach [50-52] that provides exact asymptotic solutions for the distribution.”
From Network geometry with flavor: From complexity to quantum geometry (2016) · cites this paper as [50]
In the citing paper
“Using the master equation approach [50-52] , it is possible to derive the exact distribution for the generalized degrees. We indicate with N t, [1] d,δ ( k ) the average number of δ -faces that at time t have generalized degree k d,δ = k . The master equation[50-52] for N t, [1] d,δ ( k ) reads”
From Network geometry with flavor: From complexity to quantum geometry (2016) · cites this paper as [50]
In the citing paper
“In NGF with flavor s = 1 and β = 0 each ( d -1) -face α ∈ S d,d -1 has a probability to be selected proportional to its generalized degree k d,d -1 ( α ). In fact the probability Π [1] α defined in Eq. ( S -5) includes an explicit preferential attachment mechanism [50-52, 60] as is given by”
From Network geometry with flavor: From complexity to quantum geometry (2016) · cites this paper as [50]
In the citing paper
“Strong clustering is another structural property often observed in complex networks: average clustering in random graphs of similar size and average degree is lower by orders of magnitude8910.”
From Network Cosmology (2012) · cites this paper as [8]
In the citing paper
“In many (but not all) complex networks the degree distribution is also a power law with γ close to 28910.”
From Network Cosmology (2012) · cites this paper as [8]
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Metadata
- Authors
- Dorogovtsev, S. N., & Mendes, J. F. F.
- Venue
- Oxford University Press eBooks
- Publisher
- Oxford University Press
- Published
- 2003-01-16
- OpenAlex
- W4210901545
- Cited by
- 1,563
- References
- 0
- Citations by year
- 2026: 2 · 2025: 17 · 2024: 16 · 2023: 27 · 2022: 11 · 2021: 29 · 2020: 31 · 2019: 26 · 2018: 48 · 2017: 30 · 2016: 50 · 2015: 74 · 2014: 73 · 2013: 90 · 2012: 105
- FWCI
- 25.00
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Oxford University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Graph theory and applications
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Keywords
- network evolution, network structure, complex networks, internet, World Wide Web, communication networks
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