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The clustering coefficient and the diameter of small-world networks

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Abstract

The small-world network, proposed by Watts and Strogatz, has been extensively studied for the past over ten years. In this paper, a generalized small-world network is proposed, which extends several small-world network models. Furthermore, some properties of a special type of generalized small-world network with given expectation of edge numbers have been investigated, such as the degree distribution and the isoperimetric number. These results are used to present a lower and an upper bounds for the clustering coefficient and the diameter of the given edge number expectation generalized small-world network, respectively. In other words, we prove mathematically that the given edge number expectation generalized small-world network possesses large clustering coefficient and small diameter.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, P. R. China

    Lei Gu

  2. College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, P. R. China

    Hui Lin Huang

  3. Department of Mathematics and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, P. R. China

    Xiao Dong Zhang

Authors
  1. Lei Gu
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  2. Hui Lin Huang
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  3. Xiao Dong Zhang
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Correspondence to Lei Gu.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 10971137 and 11271256), National Basic Research Program of China 973 Program (Grant No. 2006CB805900) and the Grant of Science and Technology Commission of Shanghai Municipality (STCSM No. 09XD1402500)

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Gu, L., Huang, H.L. & Zhang, X.D. The clustering coefficient and the diameter of small-world networks. Acta. Math. Sin.-English Ser. 29, 199–208 (2013). https://doi.org/10.1007/s10114-012-0387-6

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  • DOI: https://doi.org/10.1007/s10114-012-0387-6

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