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Computing the generalized dimensions Dq of a complex network requires covering the network by a minimal number of “boxes” of size s. We show that the current definition of Dq is ambiguous, since there are in general multiple minimal coverings of size s. We resolve the ambiguity by first computing, for each s, the minimal covering that is summarized by the lexicographically minimal vector x(s). We...
Computing the generalized dimensions Dq of a complex network requires covering the network by a minimal number of “boxes” of size s, for a range of s. We show that, unlike the case for a geometric multifractal, for a complex network the shape of the Dq vs. q curve can be monotone increasing, or monotone decreasing, or even have both a local maximum and a local minimum, depending on the range of box...
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