Percolation on spatial anisotropic networks

TL;DR

This paper introduces a model for spatial networks with anisotropy, analyzing how anisotropic alignment affects network robustness and percolation properties, revealing that anisotropy reduces resilience but does not alter the critical exponent in 2D lattices.

Contribution

The study generalizes existing isotropic spatial network models by incorporating anisotropy, and investigates its impact on network robustness and critical phenomena.

Findings

Anisotropy decreases network robustness.

Critical exponent $ u$ remains unchanged by anisotropy.

Anisotropic networks are less resilient under percolation.

Abstract

Many realistic systems such as infrastructures are characterized by spatial structure and anisotropic alignment. Here we propose and study a model for dealing with such characteristics by introducing a parameter that controls the strength of the anisotropy in the spatial network. This parameter is added to an existing isotropic model used to describe networks under spatial constraints, thus generalizing the spatial model to take into account both spatial and anisotropic features. We study the resilience of such networks by using a percolation process and find that anisotropy has a negative impact on a network's robustness. In addition, our results suggest that the anisotropy in this model does not affect the critical exponent of the correlation length, $\nu$, which remains the same as the known $\nu$ in 2D isotropic lattices.