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Cited by 2,160Complex Network Analysis TechniquesComplex Systems and Time Series AnalysisGraph theory and applications

Hierarchical organization in complex networks

Open access
Ravasz, Erzsébet, Barabási, Albert-László·2003·Physical Review E
DOI 10.1103/physreve.67.026112
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Abstract

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology. In hierarchical networks, the degree of clustering characterizing the different groups follows a strict scaling law, which can be used to identify the presence of a hierarchical organization in real networks. We find that several real networks, such as the Worldwideweb, actor network, the Internet at the domain level, and the semantic web obey this scaling law, indicating that hierarchy is a fundamental characteristic of many complex systems.

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Crossref · 10.1103/physreve.67.026112

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2 of 2 references verified0 citation errors · 0 not checkable

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  • The existence of power-law distributions in datasets can often be traced back to hierarchical structures.

    “the existence of power-law distributions in datasets can often be traced back to hierarchical structures [25]”

    From Poincaré Embeddings for Learning Hierarchical Representations (2017) · cites this paper as [25]

    The paper’s opening section (p. 1) says that the scale-free properties of several real networks are a consequence of hierarchical organization, and its hierarchical model has a power-law degree distribution (Section I, p. 2). The claim extends that finding from network degree distributions to power-law distributions in datasets generally, which the paper does not establish. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • Many complex symbolic datasets exhibit a latent hierarchical structure.

    “complex symbolic datasets often exhibit a latent hierarchical structure”

    From Poincaré Embeddings for Learning Hierarchical Representations (2017) · cites this paper as [25]

    The paper reports hierarchical organization in several complex networks, including a language network linking synonymous words (Section II, p. 3). This supports the possibility of latent hierarchy in symbolic data, but it does not establish that complex symbolic datasets in general often exhibit it. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

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Cites

Flagged first, then by citations

Research works printed but not linked: 17

  1. [4]A. Wagner and D. A. Fell, Proc. R. Soc. Lond. B. Biol. Sci. 268 , 1803 (2001).
  2. [10]B. Bollob´ as, Random Graphs (Academic Press, London, 1985).
  3. [14]M. E. J. Newman, Proc. Nat. Acad. Sci. U.S.A. 98 , 404 (2001).
  4. [16]A.-L. Barab´ asi, H. Jeong, Z. N´ eda, E. Ravasz, A. Schubert, and T. Vicsek, Physica A (in press) (2002).
  5. [18]G. W. Flake, S. Lawrence, and C. L. Giles, in Proceedings of the Sixth International Conference on Knowledge Discovery and Data Mining (ACM, Boston, MA, USA, 2000), p. 150.
  6. [19]L. A. Adamic and E. Adar (2000), preprint, http://hpl.hp.com/shl/papers/web10/index.html .
  7. [21]S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Los Alamos Archive cond-mat/0112143 (2001). · arXiv
  8. [22]S. Jung, S. Kim, and B. Kahng, A geometric fractal growth model for scale free networks (2001), Los Alamos Archive cond-mat/0112361. · arXiv
  9. [25]L. A. N. Amaral, A. Scala, M. Barth´ el´ emy, and H. E. Stanley, Proc. Nact. Acad. Sci. U.S.A 97 , 11 149 (2000).
  10. [26]R. F. i Cancho and R. V. Sol´ e, Proc. R. Soc. Lond. B. 268 , 2261 (2001).
  11. [27]S. Yook, H. Jeong, and A.-L. Barab´ asi (2002), Preprint.
  12. [29]S. N. Dorogovtsev and J. F. F. Mendes, Proc. R. Soc. Lond. B. 268 , 2603 (2001).
  13. [30]J.-P. Eckmann and E. Moses, Proc. Nact. Acad. Sci. U.S.A 99 , 5825 (2002).
  14. [34]A. V´ azquez, R. Pastor-Satorras, and A. Vespignani, Internet topology at the router and autonomous system level (2002), Los Alamos Archive cond-mat/0206084. · arXiv
  15. [35]R. Govindan and H. Tangmunarunkit, in Proceedings of IEEE INFOCOM 2000, Tel Aviv, Israel (IEEE, Piscataway, N. J., 2000), vol. 3, p. 1371.
  16. [36]S. H. Yook, H. Jeong, and A.-L. Barab´ asi (2002), Los Alamos Archive cond-mat/0107417. · arXiv
  17. [42]Note, however, that as new nodes tend to connect to nodes that were added to the network shortly before them, the model generates a close to one dimensional structure in time. See e.g. A. V´ azquez, Y. Moreno, M. Bogu˜ n´ a, R. Pastor-Satorras and A. Vespignani, Topology and correlations in structured scale-free networks (2002), preprint.

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Authors
Ravasz, E., & Barabási, A.-L.
Venue
Physical Review E
Publisher
American Physical Society (APS)
Published
2003-02-14
Volume
67
Issue
2
Pages
026112-026112
ISSN
  • 1063-651X (ISSN-L)
  • 1095-3787
DOI
10.1103/physreve.67.026112
OpenAlex
W2018049970
Cited by
2,160
References
2
Citations by year
2026: 38 · 2025: 61 · 2024: 62 · 2023: 58 · 2022: 104 · 2021: 147 · 2020: 109 · 2019: 102 · 2018: 117 · 2017: 115 · 2016: 90 · 2015: 102 · 2014: 95 · 2013: 112 · 2012: 103
FWCI
48.10
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Digital Repository Service (Northeastern University) (submittedVersion)
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 › Geometry and Topology › Graph theory and applications
Keywords
hierarchy, complex networks, scale-free networks, clustering coefficient, scaling laws, network topology, World Wide Web, actor networks, semantic web, community structure
MeSH terms
Models, Theoretical, Social Support, Stochastic Processes, Cluster Analysis, Internet

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