Fractal Dimensions of Networks

The study of fractal dimensions of networks has been researched for over a century, and the book provides a unified treatment of this topic. It covers the classical theory and algorithms for the box counting dimension for sets and applies them to networks, studying all major fractal dimensions and including worked examples, applications, and exercises.

Format: Paperback / softback
Length: 524 pages
Publication date: 08 July 2021
Publisher: Springer Nature Switzerland AG

The fascination with the fractal dimensions of networks has its roots in a rich tapestry of research spanning over a century. This captivating field has emerged as a culmination of tireless exploration and theoretical advancements. Fractal Dimensions of Networks seamlessly weaves together the principles and techniques for computing fractal dimensions of networks with the foundational theory of dimensions applied to geometric objects. This comprehensive book serves as a guiding light, offering a unified treatment of fractal dimensions for both sets and networks.

To achieve this lofty objective, the book takes a sequential approach. It begins by meticulously presenting the theory and algorithms for sets, employing an abundance of examples and illustrations to elucidate key concepts. This foundational foundation enables the book to seamlessly extend its reach to networks, showcasing how the theory and methodologies have been applied to unravel the intricate structures of these complex systems. Thus, the book unfolds the classical theory and algorithms for the box counting dimension, a fundamental measure of fractal dimensions for sets. It then delves into the realm of networks, presenting the box counting dimension as a key metric for understanding their intricate properties.

Within the pages of this remarkable work, the exploration of diverse fractal dimensions is undertaken. The correlation dimension, a measure of the linear relationship between variables, is examined in depth. The information dimension, quantifying the amount of information contained within a system, is explored. The Hausdorff dimension, which captures the complexity of a set, is scrutinized. Additionally, the multifractal spectrum, a rich tapestry of fractal structures, is unveiled. Furthermore, the book delves into the realm of lesser-known dimensions, shedding light on their unique characteristics and applications.

To enhance the understanding and practical application of these concepts, detailed algorithm descriptions are accompanied by comprehensive worked examples. These examples not only illustrate the theoretical underpinnings but also provide practical insights into the real-world applications of fractal dimensions. Furthermore, the book presents a multitude of applications spanning various fields, ranging from computer science and mathematics to biology and social sciences. These applications showcase the versatility and significance of fractal dimensions in understanding complex systems.

To reinforce the learning experience, an array of exercises is included, catering to students and researchers alike. These exercises span a range of difficulties, from easy to research-level, allowing individuals to deepen their understanding and apply the learned concepts in practical scenarios.

In summary, Fractal Dimensions of Networks stands as a monumental achievement, encapsulating a century of research and theoretical advancements. It provides a comprehensive and unified treatment of fractal dimensions for sets and networks, offering a deep understanding of the intricate structures and properties of these complex systems. By presenting the classical theory and algorithms, accompanied by practical examples and engaging exercises, this book empowers students, researchers, and practitioners to explore the fascinating world of fractal dimensions and unlock the hidden insights they hold.

Weight: 1326g
Dimension: 279 x 210 (mm)
ISBN-13: 9783030431716
Edition number: 1st ed. 2020