Networks
Abstract
The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.
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The distribution of degrees of vertices in a random network generally follows the Poisson distribution.
“The distribution of degrees of vertices in a complex network and a random network generally follows the power-law distribution and Poisson distribution, respectively (Barabási and Albert, 1999; Newman, 2003, 2010).”
From Syntactic Networks of Interlanguage Across L2 Modalities and Proficiency Levels (2021) · cites this paper as Newman, 2010
The distribution of degrees of vertices in a complex network generally follows the power-law distribution.
“The distribution of degrees of vertices in a complex network and a random network generally follows the power-law distribution and Poisson distribution, respectively (Barabási and Albert, 1999; Newman, 2003, 2010).”
From Syntactic Networks of Interlanguage Across L2 Modalities and Proficiency Levels (2021) · cites this paper as Newman, 2010
A wide range of measures developed in network and graph theories could assist in understanding urban evolution, including networks' structure, density, resilience, connectedness, hierarchy, modularity, or clustering.
“A wide range of measures, developed in network and graph theories, could assist in understanding urban evolution -networks' structure, their density, resilience, connectedness, hierarchy, modularity, or clustering works' structure, their density, resilience, connectedness, hierarchy, modularity or clustering (Arcaute et al.,2015;Barthelemy,2015;Newman,2010), though not discussed here in details.”
From POI VizNet: New QGIS Tool to construct Visibility Networks in Cities (2024) · cites this paper as Newman,2010
Small-world and scale-free properties allow classifying different networks in terms of their robustness, efficiency and heterogeneity.
“Small-world and scale-free properties allow classifying different networks in terms of their robustness, efficiency and heterogeneity (Barthelemy 2011;Newman 2010).”
From A Network Approach to Link Visibility and Urban Activity Location (2018) · cites this paper as Newman 2010
Networks can be modeled as graphs consisting of elements that exhibit specific interactions with other elements.
“One way to model such networks is as graphs consisting of elements that exhibit specific interactions with other elements [60–64].”
From Multi-omics approaches to disease (2017) · cites this paper as [62]
Using the master equation approach, the generalized degrees k_{d,δ} can follow either binomial, exponential, or power-law distributions depending on the dimensions d and δ and on the flavor s.
“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 [51]
For deriving results at β=0, the master equation approach provides exact asymptotic solutions for the distribution.
“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 [51]
In NGF with flavor s=1 and β=0 each (d-1)-face α has a probability to be selected proportional to its generalized degree k_{d,d-1}(α). The probability Π^{[1]}_α includes an explicit preferential attachment mechanism.
“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 [51]
Using the master equation approach, it is possible to derive the exact distribution for the generalized degrees. We find the corresponding distribution.
“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 [51]
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“The distribution of degrees of vertices in a complex network and a random network generally follows the powerlaw distribution and Poisson distribution, respectively (Barabási and Albert, 1999; Newman, 2003, 2010).”
BackgroundOpen Challenges in Multi-Agent Security: Towards Secure Systems of Interacting AI Agents
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“First, the inherent unpredictability and nonlinear state transitions at the edge of chaos hinder traditional verification and static analysis techniques, leaving vulnerabilities that adversaries can exploit (Newman, 2018a).”
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- Authors
- Newman, M.
- Corresponding author
- Newman, Mark
- ORCID
- Newman, Mark
- Venue
- Oxford University Press eBooks
- Publisher
- Oxford University Press
- Published
- 2010-03-25
- OpenAlex
- W4238452917
- Cited by
- 6,595
- References
- 0
- Citations by year
- 2026: 283 · 2025: 288 · 2024: 248 · 2023: 301 · 2022: 355 · 2021: 468 · 2020: 508 · 2019: 567 · 2018: 670 · 2017: 620 · 2016: 599 · 2015: 515 · 2014: 446 · 2013: 340 · 2012: 243
- FWCI
- 57.25
- 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
- Social Sciences › Sociology and Political Science › Contemporary Social and Educational Issues
- Social Sciences › Business, Management and Accounting › Strategy and Management › Business Strategy and Innovation
- Keywords
- networks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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