Fractal Dimensions of Networks
Springer International Publishing (Verlag)
978-3-030-43168-6 (ISBN)
Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the "classic" theory of dimensions of geometric objects.
The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.
Eric Rosenberg is a Visiting Professor in the Department of Industrial and Systems Engineering at Rutgers, The State University of New Jersey. He was previously at AT&T Labs in Middletown, New Jersey; at Bell Labs in Holmdel, New Jersey, and has taught undergraduate and graduate courses in optimization at Princeton University and New Jersey Institute of Technology. Dr. Rosenberg has authored or co-authored 17 patents and has published in the areas of convex analysis and nonlinearly constrained optimization, computer aided design of integrated circuits and printed wire boards, telecommunications network design and routing, and fractal dimensions of networks. He is the author of A Survey of Fractal Dimensions of Networks , and A Primer of Multicast Routing, both of which are Springer Briefs in Computer Science.
1. Introduction.- 2. Networks: Introductory Material.- 3. Fractals: Introductory Material.- 4. Topological and Box Counting Dimensions.- 5. Hausdor , Similarity, and Packing Dimensions.- 6. Computing the Box Counting Dimension.- 7. Network Box Counting Dimension.- 8. Network Box Counting Heuristics.- 9. Correlation Dimension.- 10. Computing the Correlation Dimension.- 11. Network Correlation Dimension.- 12. Dimensions of Infinite Networks.- 13. Similarity Dimension of Infinite Networks.- 14. Information Dimension.- 15. Network Information Dimension.- 16. Generalized Dimensions and Multifractals.- 17. Multifractal Networks.- 18. Generalized Hausdor Dimensions of Networks.- 19. Lacunarity.- 20. Other Dimensions.- 21. Coarse Graining and Renormalization.- 22. Other Network Dimensions.- 23. Supplemental Material.-
| Erscheinungsdatum | 09.07.2020 |
|---|---|
| Zusatzinfo | XX, 524 p. 224 illus., 147 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 210 x 279 mm |
| Gewicht | 1564 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Netzwerke |
| Schlagworte | box counting • complex networks • correlation dimension • fractal dimensions • information dimension • Multifractals • network science • Random Networks • Scale-free networks • Self-similarity • small-world networks • topological dimension |
| ISBN-10 | 3-030-43168-1 / 3030431681 |
| ISBN-13 | 978-3-030-43168-6 / 9783030431686 |
| Zustand | Neuware |
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