A Survey of Fractal Dimensions of Networks

Beschreibung

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.

Required reading for anyone involved with the active research area of complex networks Reviews the theory and computation of the most important fractal dimensions, 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 multifractal networks), and the sandbox method (for approximating the generalized dimensions)

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Eric Rosenberg

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

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“This book presents an updated survey on the fractal dimensions of networks. It focuses on the theory and computation of some important fractal dimensions such as box counting dimension, correlation dimension, mass dimension, transfinite fractal dimension, information dimension, and generalized dimension. The book is suitable for readers with some basic knowledge on limit, derivatives, shortest path algorithm, as well as duality theory in linear programming. There are plenty of figures and sketches throughout the book, which make it fairly readable.” (Yilun Shang, zbMath 1414.05001, 2019)
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