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Hyperbolic mapping of complex networks based on community information

Author

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  • Wang, Zuxi
  • Li, Qingguang
  • Jin, Fengdong
  • Xiong, Wei
  • Wu, Yao

Abstract

To improve the hyperbolic mapping methods both in terms of accuracy and running time, a novel mapping method called Community and Hyperbolic Mapping (CHM) is proposed based on community information in this paper. Firstly, an index called Community Intimacy (CI) is presented to measure the adjacency relationship between the communities, based on which a community ordering algorithm is introduced. According to the proposed Community-Sector hypothesis, which supposes that most nodes of one community gather in a same sector in hyperbolic space, CHM maps the ordered communities into hyperbolic space, and then the angular coordinates of nodes are randomly initialized within the sector that they belong to. Therefore, all the network nodes are so far mapped to hyperbolic space, and then the initialized angular coordinates can be optimized by employing the information of all nodes, which can greatly improve the algorithm precision. By applying the proposed dual-layer angle sampling method in the optimization procedure, CHM reduces the time complexity to O(n2). The experiments show that our algorithm outperforms the state-of-the-art methods.

Suggested Citation

  • Wang, Zuxi & Li, Qingguang & Jin, Fengdong & Xiong, Wei & Wu, Yao, 2016. "Hyperbolic mapping of complex networks based on community information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 104-119.
    • Handle: RePEc:eee:phsmap:v:455:y:2016:i:c:p:104-119
    DOI: 10.1016/j.physa.2016.02.015
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    References listed on IDEAS

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    1. Fragkiskos Papadopoulos & Maksim Kitsak & M. Ángeles Serrano & Marián Boguñá & Dmitri Krioukov, 2012. "Popularity versus similarity in growing networks," Nature, Nature, vol. 489(7417), pages 537-540, September.
    2. Ma, Lili & Jiang, Xin & Wu, Kaiyuan & Zhang, Zhanli & Tang, Shaoting & Zheng, Zhiming, 2012. "Surveying network community structure in the hidden metric space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 371-378.
    3. Marián Boguñá & Fragkiskos Papadopoulos & Dmitri Krioukov, 2010. "Sustaining the Internet with hyperbolic mapping," Nature Communications, Nature, vol. 1(1), pages 1-8, December.
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    Cited by:

    1. Li, Jichao & Ge, Bingfeng & Yang, Kewei & Chen, Yingwu & Tan, Yuejin, 2017. "Meta-path based heterogeneous combat network link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 507-523.
    2. Balogh, Sámuel G. & Palla, Gergely, 2024. "Intra-community link formation and modularity in ultracold growing hyperbolic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 642(C).
    3. Moradi, Mehdi & Parsa, Saeed, 2019. "An evolutionary method for community detection using a novel local search strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 457-475.
    4. Yao, Yabing & Zhang, Ruisheng & Yang, Fan & Tang, Jianxin & Yuan, Yongna & Hu, Rongjing, 2018. "Link prediction in complex networks based on the interactions among paths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 52-67.
    5. Yin, Likang & Zheng, Haoyang & Bian, Tian & Deng, Yong, 2017. "An evidential link prediction method and link predictability based on Shannon entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 699-712.

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