Irreducible network backbones: unbiased graph filtering via maximum entropy

TL;DR

This paper introduces a maximum-entropy based method for filtering networks to identify irreducible, essential links that cannot be inferred from local node properties, revealing hidden structural patterns.

Contribution

The authors develop a rigorous, unbiased filtering technique that guarantees the extracted network backbone is irreducible to local node properties using an exact maximum-entropy formulation.

Findings

Uncovers hidden essential network backbones in various real-world systems.

Recovers the hub-and-spoke structure of the US airport network.

Identifies higher-order wiring principles beyond local constraints.

Abstract

Networks provide an informative, yet non-redundant description of complex systems only if links represent truly dyadic relationships that cannot be directly traced back to node-specific properties such as size, importance, or coordinates in some embedding space. In any real-world network, some links may be reducible, and others irreducible, to such local properties. This dichotomy persists despite the steady increase in data availability and resolution, which actually determines an even stronger need for filtering techniques aimed at discerning essential links from non-essential ones. Here we introduce a rigorous method that, for any desired level of statistical significance, outputs the network backbone that is irreducible to the local properties of nodes, i.e. their degrees and strengths. Unlike previous approaches, our method employs an exact maximum-entropy formulation guaranteeing that the filtered network encodes only the links that cannot be inferred from local information. Extensive empirical analysis confirms that this approach uncovers essential backbones that are otherwise hidden amidst many redundant relationships and inaccessible to other methods. For instance, we retrieve the hub-and-spoke skeleton of the US airport network and many specialised patterns of international trade. Being irreducible to local transportation and economic constraints of supply and demand, these backbones single out genuinely higher-order wiring principles.