Percolation transition in correlated static model

TL;DR

This paper introduces a correlated static network model with assortative degree correlations and studies its percolation transition, revealing critical phenomena influenced by structural correlations.

Contribution

It presents a novel correlated static model and analyzes how assortative degree correlations affect the percolation transition in complex networks.

Findings

Percolation transition exhibits weak singularity in mean cluster size.

Power-law scaling observed in the percolation order parameter.

Cluster size distribution follows power-law in the non-percolating phase.

Abstract

We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network undergoes a percolation transition. The percolation transition is characterized by a weak singular behavior of the mean cluster size and power-law scalings of the percolation order parameter and the cluster size distribution in the entire non-percolating phase. These results suggest that the assortative degree-degree correlation generates a global structural correlation which is relevant to the percolation critical phenomena of complex networks.