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

  • Lorenzo von RitterEmail author
  • Michael E. Houle
  • Stephan Günnemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11223)

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.

Keywords

Intrinsic dimensionality Graph Degree Estimation 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Lorenzo von Ritter
    • 1
    • 2
    Email author
  • Michael E. Houle
    • 1
  • Stephan Günnemann
    • 2
  1. 1.National Institute of InformaticsChiyoda-kuJapan
  2. 2.Technical University of MunichMunichGermany

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