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A random geometric graph built on a time-varying Riemannian manifold

Author

Listed:
  • Xie, Zheng
  • Zhu, Jiang
  • Kong, Dexing
  • Li, Jianping

Abstract

The theory of random geometric graph enables the study of complex networks through geometry. To analyze evolutionary networks, time-varying geometries are needed. Solutions of the generalized hyperbolic geometric flow are such geometries. Here we propose a scale-free network model, which is a random geometric graph on a two dimensional disc. The metric of the disc is a Ricci flat solution of the flow. The model is used to physically simulate the growth and aggregation of a type of cancer cell.

Suggested Citation

  • Xie, Zheng & Zhu, Jiang & Kong, Dexing & Li, Jianping, 2015. "A random geometric graph built on a time-varying Riemannian manifold," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 492-498.
    • Handle: RePEc:eee:phsmap:v:436:y:2015:i:c:p:492-498
    DOI: 10.1016/j.physa.2015.05.076
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    References listed on IDEAS

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    1. Zheng Xie & Zhenzheng Ouyang & Pengyuan Zhang & Dongyun Yi & Dexing Kong, 2015. "Modeling the Citation Network by Network Cosmology," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-13, March.
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    Cited by:

    1. Zheng Xie & Xiaojun Duan & Zhenzheng Ouyang & Pengyuan Zhang, 2015. "Quantitative Analysis of the Interdisciplinarity of Applied Mathematics," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-11, September.
    2. Xie, Zheng & Ouyang, Zhenzheng & Li, Jianping, 2016. "A geometric graph model for coauthorship networks," Journal of Informetrics, Elsevier, vol. 10(1), pages 299-311.
    3. Xie, Zheng & Ouyang, Zhenzheng & Liu, Qi & Li, Jianping, 2016. "A geometric graph model for citation networks of exponentially growing scientific papers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 167-175.
    4. Clough, James R. & Evans, Tim S., 2016. "What is the dimension of citation space?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 235-247.

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