Topologic distance in the Lucena network

Darlan A. Moreira and Gilberto Corso ()
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Darlan A. Moreira: Escola de Ciências e Tecnologia, Campus Central Universidade Federal do Rio Grande do Norte
Gilberto Corso: Departamento de Biofísica e Farmacologia, Centro de Biociências, Universidade Federal do Rio Grande do Norte

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 5, 1-5

Abstract: Abstract The Lucena network (LN) is the dual of a multifractal partition of the square. We analyze the relation between the typical topologic distance l and the number of vertices N of the LN. The multifractal partition has one parameter ρ which controls the geometrical asymmetry of the multifractal. In the limit of ρ → 1 the blocks of the partition are squared, the connections amont the blocks are short range, the LN is more regular and the relation l ∝ √N is observed. For the limit ρ → 0 the blocks are strongly asymmetric, long range connections appear, and the topologic distance follows l ∝ (log N) α , a weak small world phenomenon. For any network size we calculate analytically the size of the minimum distance l min (ρ → 0) and the maximal distance l max (ρ → 1). The distance in the weak small world regime is calculated using the number of vertices inside a radius of length l and taking into account the network average connectivity and the exponent α.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2016-60669-6

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