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Scan Statistics on Graphs and Networks

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Abstract

This article summarizes modern research of scan statistics on graphs and networks. These statistics arise naturally in the scanning of time and space looking for clusters of anomalous entities or events. We review theories and methodologies of constructing scan statistics for both static and dynamic graphs, in both purely spatial and spatio temporal frameworks. Computation of graph-structured scan statistics is challenging, and usually leads to NP-hard problems. We also review several popular convex approximation algorithms for computing scan statistics in this article.

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Notes

  1. 1.

    The chromatic number is the smallest number of colors needed to color a graph such that no two adjacent vertices share the same color.

  2. 2.

    The likelihood ratio test is known to be the uniformly most powerful test according to the Neyman-Pearson Lemma.

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Authors and Affiliations

  1. Department of Statistics, University of Connecticut, Storrs, CT, USA

    Panpan Zhang & Joseph Glaz

Authors
  1. Panpan Zhang
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  2. Joseph Glaz
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Correspondence to Panpan Zhang .

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Editors and Affiliations

  1. University of Connecticut Dept. Statistics, Storrs, Connecticut, USA

    Joseph Glaz

  2. University of Pireaus Dept. Statistics & Insurance Sciences, Piraeus, Greece

    Markos V. Koutras

Section Editor information

  1. Dept. of Statistics and Insurance Science, University of Piraeus, 18534, Piraeus, Greece

    Markos V. Koutras

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Zhang, P., Glaz, J. (2018). Scan Statistics on Graphs and Networks. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_43-1

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  • DOI: https://doi.org/10.1007/978-1-4614-8414-1_43-1

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  • Print ISBN: 978-1-4614-8414-1

  • Online ISBN: 978-1-4614-8414-1

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