Percolation on random networks with arbitrary k-core structure

TL;DR

This paper introduces a new theoretical model, the Hard-core Random Network, that accurately predicts percolation behavior in complex networks with arbitrary k-core structures, outperforming existing models.

Contribution

The paper presents the Hard-core Random Network model, integrating k-core structure into a random network framework and providing exact solutions for bond percolation.

Findings

The HRN model accurately predicts percolation thresholds.

It outperforms existing models in real network analysis.

The approach requires less input information.

Abstract

The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with selected databases reveals that our approach performs better than existing models, while requiring less input information.