Percolation and the effective structure of complex networks

TL;DR

This paper introduces an intensive network modeling approach that accurately predicts bond percolation outcomes by considering node degree and core-periphery position, bridging the gap between detailed and simplified models.

Contribution

It presents a novel intensive description method that matches message passing accuracy for percolation, emphasizing the importance of long-range correlations in network structure.

Findings

The approach yields predictions nearly identical to message passing.

It effectively captures long-range correlations in networks.

The method simplifies complex network data while maintaining accuracy.

Abstract

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency matrix) description of the network structure. While extensive approaches---such as the state-of-the-art Message Passing Approach---typically yield more accurate predictions, intensive approaches provide crucial insights on the role played by any given structural property in the outcome of dynamical processes. Here we introduce an intensive description that yields almost identical predictions to the ones obtained with MPA for bond percolation. Our approach distinguishes nodes according to two simple statistics: their degree and their position in the core-periphery organization of the network. Our near-exact predictions highlight how accurately capturing the long-range correlations in network structures allows to easily and effectively compress real complex network data.