  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.
