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A Survey of Fractal Dimensions of Networks

  • EricĀ Rosenberg

Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Eric Rosenberg
    Pages 1-6
  3. Eric Rosenberg
    Pages 7-11
  4. Eric Rosenberg
    Pages 13-27
  5. Eric Rosenberg
    Pages 29-37
  6. Eric Rosenberg
    Pages 39-44
  7. Eric Rosenberg
    Pages 45-50
  8. Eric Rosenberg
    Pages 55-59
  9. Eric Rosenberg
    Pages 61-67
  10. Eric Rosenberg
    Pages 69-75
  11. Eric Rosenberg
    Pages 77-79
  12. Back Matter
    Pages 81-84

About this book

Introduction

Many different fractal dimensions have been proposed for networks. In A Survey of Fractal Dimensions of Networks the theory and computation of the most important of these dimensions are reviewed, including the box counting dimension, the correlation dimension, the mass dimension, the transfinite fractal dimension, the information dimension, the generalized dimensions (which provide a way to describe multifractals), and the sandbox method (for approximating the generalized dimensions). The book describes the use of diameter-based and radius-based boxes, and presents several heuristic methods for box counting, including greedy coloring, random sequential node burning, and a method for computing a lower bound. We also discuss very recent results on resolving ambiguity in the calculation of the information dimension and the generalized dimensions, and on the non-monotonicity of the generalized dimensions. 

Anyone interested in the theory and application of networks will want to read this Brief. This includes anyone studying, e.g., social networks, telecommunications networks, transportation networks, ecological networks, food chain networks, network models of the brain, or financial networks.

Keywords

complex network fractal multifractal fractal dimensions box counting generalized dimensions correlation dimension information dimension entropy partition function graph coloring

Authors and affiliations

  • EricĀ Rosenberg
    • 1
  1. 1.AT&T LabsMiddletownUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-90047-6
  • Copyright Information The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-90046-9
  • Online ISBN 978-3-319-90047-6
  • Series Print ISSN 2191-5768
  • Series Online ISSN 2191-5776
  • Buy this book on publisher's site
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