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Intrinsic Degree: An Estimator of the Local Growth Rate in Graphs

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Similarity Search and Applications (SISAP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11223))

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Abstract

The neighborhood size of a query node in a graph often grows exponentially with the distance to the node, making a neighborhood search prohibitively expensive even for small distances. Estimating the growth rate of the neighborhood size is therefore an important task in order to determine an appropriate distance for which the number of traversed nodes during the search will be feasible. In this work, we present the intrinsic degree model, which captures the growth rate of exponential functions through the analysis of the infinitesimal vicinity of the origin. We further derive an estimator which allows to apply the intrinsic degree model to graphs. In particular, we can locally estimate the growth rate of the neighborhood size by observing the close neighborhood of some query points in a graph. We evaluate the performance of the estimator through experiments on both artificial and real networks.

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Notes

  1. 1.

    Implementation from [6]: http://www.stats.ox.ac.uk/~caron/code/bnpgraph/.

  2. 2.

    https://de.mathworks.com/matlabcentral/fileexchange/11947-b-a-scale-free-network-generation-and-visualization.

  3. 3.

    https://www.cise.ufl.edu/research/sparse/matrices/Pajek/yeast.html.

  4. 4.

    https://snap.stanford.edu/data/email-Enron.html.

  5. 5.

    https://www.cise.ufl.edu/research/sparse/matrices/Pajek/IMDB.html.

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Acknowledgments

This research was supported in part by the Technical University of Munich - Institute for Advanced Study, funded by the German Excellence Initiative and the European Union Seventh Framework Programme under grant agreement no 291763, co-funded by the European Union. M. E. Houle was supported by JSPS Kakenhi Kiban (B) Research Grant 18H03296.

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Authors and Affiliations

  1. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Lorenzo von Ritter & Michael E. Houle

  2. Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Lorenzo von Ritter & Stephan Günnemann

Authors
  1. Lorenzo von Ritter
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  2. Michael E. Houle
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  3. Stephan Günnemann
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Correspondence to Lorenzo von Ritter .

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Editors and Affiliations

  1. University of Geneva, Carouge, Switzerland

    Stéphane Marchand-Maillet

  2. Arizona State University, Tempe, AZ, USA

    Yasin N. Silva

  3. Center for Scientific Research and Higher Education, Ensenada, Mexico

    Edgar Chávez

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von Ritter, L., Houle, M.E., Günnemann, S. (2018). Intrinsic Degree: An Estimator of the Local Growth Rate in Graphs. In: Marchand-Maillet, S., Silva, Y., Chávez, E. (eds) Similarity Search and Applications. SISAP 2018. Lecture Notes in Computer Science(), vol 11223. Springer, Cham. https://doi.org/10.1007/978-3-030-02224-2_15

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  • DOI: https://doi.org/10.1007/978-3-030-02224-2_15

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  • Online ISBN: 978-3-030-02224-2

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