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A Survey of Fractal Dimensions of Networks (Paperback, 1st ed. 2018)
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A Survey of Fractal Dimensions of Networks (Paperback, 1st ed. 2018)
Series: SpringerBriefs in Computer Science
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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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