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The Structure and Function of Complex Networks
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Abstract. Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
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“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, 2003
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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, 2003
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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 [9]
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“Several models, based on mechanisms like preferential attachment 15 , fi tness 94 , or constrained random wiring 54 , to mention some of them, were developed to reproduce degree distributions commonly observed in empirical systems.”
From Complex networks from classical to quantum (2019) · cites this paper as [54]
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“Other risks from rewiring include 'phase transitions', where a gradual change in individual connections or network structure triggers a sudden and dramatic shift in the behaviour of the entire network (Newman, 2003, see also Section 3.4).”
From Multi-Agent Risks from Advanced AI (2025) · cites this paper as Newman, 2003
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“SNA makes it possible to understand and highlight interactions and knowledge flows between actors (Chaudhury et al. 2017;Isaac 2012;Newman 2003).”
From Scenarios for an agroecological transition of smallholder family farmers: a case study in Guadeloupe (2022) · cites this paper as Newman 2003
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“The 90–9–1 rule classifies user participation into three categories; specifically, Lurkers, Contributors, and Superusers, where 90% of actors do not participate, 9% seldom contribute, and 1% contribute significantly to the content (15, 17, 18, 22, 23).”
From Trouble with the curve: the 90-9-1 rule to measure volitional participation inequalities among Royal Canadian Mounted Police cadets during training (2024) · cites this paper as [22]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
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“The relationships between participant motivation, use, engagement, and actor status have identified participation inequalities mirroring the 80–20 Pareto principle and participation patterns such as the 90–9–1 rule (18, 21, 22).”
From Trouble with the curve: the 90-9-1 rule to measure volitional participation inequalities among Royal Canadian Mounted Police cadets during training (2024) · cites this paper as [22]
Experimental — accuracy not yet measuredIn the citing paper
“Node degree is central to network topology and a major factor in numerous other properties (Gillis and Pavlidis, 2011b;Newman, 2003).”
From Guidance for RNA-seq co-expression network construction and analysis: safety in numbers (2015) · cites this paper as Newman, 2003
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 [9]
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Metadata
- Authors
- Newman, M. E. J.
- Affiliations
- Santa Fe Institute (US)
- Corresponding author
- Newman, M. E. J.
- ORCID
- Newman, M. E. J.
- Venue
- SIAM Review
- Published
- 2003-01-01
- Volume
- 45
- Issue
- 2
- Pages
- 167-256
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2148606196
- Cited by
- 18,719
- References
- 20
- Citations by year
- 2026: 493 · 2025: 574 · 2024: 588 · 2023: 573 · 2022: 723 · 2021: 789 · 2020: 813 · 2019: 925 · 2018: 958 · 2017: 1004 · 2016: 1006 · 2015: 1053 · 2014: 1089 · 2013: 1134 · 2012: 1018
- FWCI
- 251.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- SIAM Review (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. National Science Foundation (DMS-0109086, DMS-0234188)
- James S. McDonnell Foundation and the Santa Fe Institute
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Graph theory and applications
- Keywords
- complex networks, small-world effect, degree distribution, clustering, network correlation, random graph models, network growth models, preferential attachment, dynamical processes on networks, social networks, biological networks, internet
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