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Higher order clustering coefficients in Barabási–Albert networks

Author

Listed:
  • Fronczak, Agata
  • Hołyst, Janusz A
  • Jedynak, Maciej
  • Sienkiewicz, Julian

Abstract

Higher order clustering coefficients C(x) are introduced for random networks. The coefficients express probabilities that the shortest distance between any two nearest neighbours of a certain vertex i equals x, when one neglects all paths crossing the node i. Using C(x) we found that in the Barabási–Albert (BA) model the average shortest path length in a node's neighbourhood is smaller than the equivalent quantity of the whole network and the remainder depends only on the network parameter m. Our results show that small values of the standard clustering coefficient in large BA networks are due to random character of the nearest neighbourhood of vertices in such networks.

Suggested Citation

  • Fronczak, Agata & Hołyst, Janusz A & Jedynak, Maciej & Sienkiewicz, Julian, 2002. "Higher order clustering coefficients in Barabási–Albert networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 688-694.
    • Handle: RePEc:eee:phsmap:v:316:y:2002:i:1:p:688-694
    DOI: 10.1016/S0378-4371(02)01336-5
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    Cited by:

    1. Lawford, Steve & Mehmeti, Yll, 2020. "Cliques and a new measure of clustering: With application to U.S. domestic airlines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    2. Peng Liu & Liang Gui & Huirong Wang & Muhammad Riaz, 2022. "A Two-Stage Deep-Learning Model for Link Prediction Based on Network Structure and Node Attributes," Sustainability, MDPI, vol. 14(23), pages 1-15, December.
    3. Kumar, Ajay & Singh, Shashank Sheshar & Singh, Kuldeep & Biswas, Bhaskar, 2020. "Link prediction techniques, applications, and performance: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    4. Guang Zhang & Nan He & Yanxia Dong, 2021. "A Proportional-Egalitarian Allocation Policy for Public Goods Problems with Complex Network," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    5. Jeong, Wonhee & Yu, Unjong, 2022. "Effects of quadrilateral clustering on complex contagion," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. Ergin Elmacioglu & Dongwon Lee, 2009. "Modeling idiosyncratic properties of collaboration networks revisited," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(1), pages 195-216, July.
    7. Cerqueti, Roy & Clemente, Gian Paolo & Grassi, Rosanna, 2021. "Stratified cohesiveness in complex business networks," Journal of Business Research, Elsevier, vol. 129(C), pages 515-526.

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