A Survey of Fractal Dimensions of Networks by Eric Rosenberg

Author:Eric Rosenberg
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

(5.1)

More formally, for a positive integer s and , define

(5.2)

where I(z) ≡ 1 if z > 0 and I(z) ≡ 0 otherwise. Thus C(n, s) is the number of nodes, distinct from n, whose distance from n is less than s. It follows that C(n, s)∕(N − 1) is the fraction of nodes, distinct from n, whose distance from n is less than s. We have C(n, 1) = 0, since no node distinct from n has distance less than 1 from n. Also, for each n and s > Δ we have C(n, s) = N − 1. The correlation sum C(s) is defined by

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