Topologic distance in the Lucena network

• Autor(a) principal: Moreira, Darlan Araújo
• Data de Publicação: 2016
• Outros Autores: Corso, Gilberto
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRN
• Texto Completo: https://repositorio.ufrn.br/handle/123456789/30639
• topic: Topologic; Lucena; Network

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 lmin (ρ → 0) and the maximal distance lmax (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