Abstract

We study the statistical properties of a variety of diverse real-world networks. We present evidence of the occurrence of three classes of small-world networks: ( a ) scale-free networks, characterized by a vertex connectivity distribution that decays as a power law; ( b ) broad-scale networks, characterized by a connectivity distribution that has a power law regime followed by a sharp cutoff; and ( c ) single-scale networks, characterized by a connectivity distribution with a fast decaying tail. Moreover, we note for the classes of broad-scale and single-scale networks that there are constraints limiting the addition of new links. Our results suggest that the nature of such constraints may be the controlling factor for the emergence of different classes of networks.

Keywords

Complex networkScale-free networkLimitingVariety (cybernetics)Small-world networkDegree distributionComputer scienceEvolving networksScale (ratio)Preferential attachmentDistribution (mathematics)Vertex (graph theory)Random graphFocus (optics)Theoretical computer scienceInterdependent networksStatistical physicsMathematicsArtificial intelligencePhysicsGeographyCartographyEngineeringGraph

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Year
2000
Type
article
Volume
97
Issue
21
Pages
11149-11152
Citations
3039
Access
Closed

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Luı́s A. Nunes Amaral, Antonio Scala, Marc Barthélémy et al. (2000). Classes of small-world networks. Proceedings of the National Academy of Sciences , 97 (21) , 11149-11152. https://doi.org/10.1073/pnas.200327197

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DOI
10.1073/pnas.200327197