A planar network between short and long range behaviour

Darlan A. Moreira, Liacir dos Santos Lucena and Gilberto Corso

Physica A: Statistical Mechanics and its Applications, 2015, vol. 434, issue C, 220-225

Abstract: 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 and the PLN shares some similarities with a small world graph.

Keywords: Multifractal lattice; Spatially embedded networks; Planar graph; Fractal dimension (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:434:y:2015:i:c:p:220-225

DOI: 10.1016/j.physa.2015.03.088

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