A planar network between short and long range behaviour

作者：Moreira Darlan A; Lucena Liacir dos Santos; Corso Gilberto^*

来源：Physica A: Statistical Mechanics and Its Applications , 2015, 434: 220-225.

DOI：10.1016/j.physa.2015.03.088

• Multifractal lattice
• Spatially embedded networks
• Planar graph
• Fractal dimension

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 rho, for rho -> 1 the network resembles a symmetric regular lattice with almost none highly connected node while rho -> 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) proportional to r(-delta) with 3 < delta < 4 according to rho. For rho -> 1 we have delta close to 4 which is a signature of short range interactions, while rho -> 0 shows delta -> 3 and has long range interactions. In addition, the fractal dimension, d(f), of the PLN behaves as: for rho -> 1, d(f) = 2, the dimension of the embedding space while for rho -> 0, d(f) increases and the PLN shares some similarities with a small world graph.

• 出版日期2015-9-15