Title: Irreducible network backbones: unbiased graph filtering via maximum entropy,
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.