Percolation and the Effective Structure of Complex Networks

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 approximation - 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 the message passing approximation using bond percolation as a benchmark. 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 easy and effective compression of real complex network data.