A planar network between short and long range behaviour
We study the Projection of Lucena Network PLN: a planar network whose nodes coincide with the sites of the square lattice. The PLN has one internal parameter ρ, for ρ → 1 the network resembles a symmetric regular lattice with almost none highly connected node while ρ → 0 is more asymmetric and there...
Na minha lista:
| Principais autores: | , , |
|---|---|
| Formato: | article |
| Idioma: | English |
| Publicado em: |
Elsevier
|
| Assuntos: | |
| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/30638 |
| Tags: |
Adicionar Tag
Sem tags, seja o primeiro a adicionar uma tag!
|
| Resumo: | We study the Projection of Lucena Network PLN: a planar network whose nodes coincide with the sites of the square lattice. The PLN has one internal parameter ρ, for ρ → 1 the network resembles a symmetric regular lattice with almost none highly connected node while ρ → 0 is more asymmetric and there are several highly connected nodes. We estimate P(r), the probability of a node be connected to another node at distance r. The PLN follows the fractal scaling P(r) ∝ r−δ with 3 < δ < 4 according to ρ. For ρ → 1 we have δ close to 4 which is a signature of short range interactions, while ρ → 0 shows δ → 3 and has long range interactions. In addition, the fractal dimension, df, of the PLN behaves as: for ρ → 1, df = 2, the dimension of the embedding space while for ρ → 0, df increases end the PLN shares some similarities with a small world graph |
|---|