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.
Highlights
The structure of real complex networks lies somewhere between order and randomness [1,2,3], with the consequence that it cannot typically be fully characterized by a concise set of synthesizing observables
To obtain useful analytical results, most models of complex networks must rely on some variation of the treelike approximation, which assumes that complex networks have essentially no loops beyond some local structure of interest [9,10]
To take advantage of the mathematical tools developed for treelike approximations, we propose to limit the information given to the model by compressing complex networks into an effective tree
Summary
The structure of real complex networks lies somewhere between order and randomness [1,2,3], with the consequence that it cannot typically be fully characterized by a concise set of synthesizing observables This irreductibility explains why most theoretical approaches to model complex networks are inspired by statistical physics in that they consider ensembles of networks constrained by the values of observables (e.g., density of links, degree-degree correlations, clustering coefficient, degree or motif distribution) and otherwise organized randomly. They are intensive in network size, meaning that their complexity scales with the support of the observables (i.e., sublinearly with the numbers of nodes and links). They provide null models, of which many have led to the identification of fundamental properties characterizing the structure of real complex networks [4,5]
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