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Hyperfiniteness of Real-World Networks

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Abstract

In addition to being rich material for successful deep learning, recent rapidly exploding big data needs more sophisticated direct approaches such algorithms that are expected to run in sublinear or even constant time. In view of this situation, property testing, which has been extensively studied in recent theoretical computer science areas, has become a promising approach. The basic framework of property testing is to decide with some inaccuracy if the input data have a certain property or not by reading only some fraction of the input. Especially, for the property testing of graphs, the hyperfiniteness of graphs plays an important role, which guarantees that any graph property can be testable. This hyperfiniteness requires graphs to have a partition that satisfies some conditions, and a property testing on algorithms that are run on those partitioned graphs. In this paper, we try to obtain such ideal partitions that satisfy hyperfiniteness by implementing an efficient partition algorithm recently proposed by Levi and Ron [ACM TALG, 2015]. Our experiments are performed mainly on real-world networks with the aim of bringing the theoretical results of property testing into practical use for big data analyses. As a result, we observed what would be effective for some classes of networks, which suggests great prospects of property testing in practice.

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Notes

  1. We say that a graph \(G = (V, E)\) follows power-law if for the positive real number of \(c>1\) and \(\gamma > 1\), \(\mu _i \le c\cdot |V|\cdot i^{-\gamma }\) for all i, where \(\mu _i\) is the number of vertices of degree i

  2. https://github.com/schulzchristian/KaHIP.

  3. http://snap.stanford.edu/index.html.

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Acknowledgements

This work was partially supported by JST CREST JPMJR1402.

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Authors and Affiliations

  1. Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku Sakai, Osaka, Japan

    Yutaro Honda, Yoshitaka Inoue & Yushi Uno

  2. The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo, Japan

    Hiro Ito

  3. University of Hyogo, 8-2-1 Gakuennishi-cho, Nishi-ku, Kobe, Japan

    Munehiko Sasajima & Junichi Teruyama

Authors
  1. Yutaro Honda
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  2. Yoshitaka Inoue
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  3. Hiro Ito
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  4. Munehiko Sasajima
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  5. Junichi Teruyama
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  6. Yushi Uno
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Correspondence to Junichi Teruyama.

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This work is supported by JST CREST Grant Number JPMJCR1402, Japan. This work is also supported by JSPS KAKENHI Grant Number 15K11985 and 17K00017.

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Honda, Y., Inoue, Y., Ito, H. et al. Hyperfiniteness of Real-World Networks. Rev Socionetwork Strat 13, 123–141 (2019). https://doi.org/10.1007/s12626-019-00051-3

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