Publicação
Topologic distance in the Lucena network
| Resumo: | 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 |
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| Autores principais: | Moreira, Darlan Araújo |
| Outros Autores: | Corso, Gilberto |
| Assunto: | Topologic Lucena Network |
| Ano: | 2020 |
| País: | Brasil |
| Tipo de documento: | artigo |
| Tipo de acesso: | unknown |
| Instituição associada: | IBICT |
| Idioma: | inglês |
| Origem: | Oasisbr |
| Resumo: | 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 |
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