| Document Type
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BL
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| Record Number
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866116
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| Main Entry
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Rosenberg, Eric
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| Title & Author
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A survey of fractal dimensions of networks /\ Eric Rosenberg.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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| Series Statement
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SpringerBriefs in computer science
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| Page. NO
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1 online resource
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| ISBN
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3319900471
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: 9783319900476
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3319900463
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9783319900469
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; About the Author; Contents; 1 Introduction; 1.1 Tables of Symbols; 1.2 Box Counting and Hausdorff Dimensions; 2 Covering a Complex Network; 2.1 Box Counting with Diameter-Based or Radius-Based Boxes; 3 Network Box Counting Heuristics; 3.1 Node Coloring Formulation; 3.2 Node Coloring for Weighted Networks; 3.3 Random Sequential Node Burning; 3.4 Set Covering Formulation and a Greedy Method; 3.5 Box Burning; 3.6 Box Counting for Scale-Free Networks; 4 Lower Bounds on Box Counting; 4.1 Mathematical Formulation; 4.2 Dual Ascent and Dual Adjustment
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4.3 Bounding the Fractal Dimension5 Correlation Dimension; 6 Mass Dimension for Infinite Networks; 6.1 Transfinite Fractal Dimension; 7 Volume and Surface Dimensions for Infinite Networks; 8 Information Dimension; 9 Generalized Dimensions; 10 Non-monotonicity of Generalized Dimensions; 11 Zeta Dimension; References
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| Abstract
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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.
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| Subject
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Fractal analysis.
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| Subject
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System analysis.
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| Subject
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COMPUTERS-- Computer Literacy.
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COMPUTERS-- Computer Science.
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COMPUTERS-- Data Processing.
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COMPUTERS-- Hardware-- General.
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COMPUTERS-- Information Technology.
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COMPUTERS-- Machine Theory.
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| Subject
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COMPUTERS-- Reference.
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| Subject
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Fractal analysis.
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| Subject
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System analysis.
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| Dewey Classification
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004.2/1
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| LC Classification
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QA402.R67 2018
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