Compressibility of complex networks

TL;DR

This paper models complex networks as information sources and uses rate-distortion theory to analyze their compressibility, revealing that hierarchical and heterogeneous networks are more amenable to compression.

Contribution

It introduces a novel framework applying rate-distortion theory to quantify network compressibility and identifies structural features that enhance compressibility.

Findings

Compressibility correlates with transitivity and degree heterogeneity.

Hierarchical, modular, and heterogeneous networks are more compressible.

The framework links network structure to information encoding capacity.

Abstract

Many complex networks depend upon biological entities for their preservation. Such entities, from human cognition to evolution, must first encode and then replicate those networks under marked resource constraints. Networks that survive are those that are amenable to constrained encoding, or, in other words, are compressible. But how compressible is a network? And what features make one network more compressible than another? Here we answer these questions by modeling networks as information sources before compressing them using rate-distortion theory. Each network yields a unique rate-distortion curve, which specifies the minimal amount of information that remains at a given scale of description. A natural definition then emerges for the compressibility of a network: the amount of information that can be removed via compression, averaged across all scales. Analyzing an array of real and model networks, we demonstrate that compressibility increases with two common network properties: transitivity (or clustering) and degree heterogeneity. These results indicate that hierarchical organization -- which is characterized by modular structure and heterogeneous degrees -- facilitates compression in complex networks. Generally, our framework sheds light on the interplay between a network's structure and its capacity to be compressed, enabling investigations into the role of compression in shaping real-world networks.