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Many complex systems can be represented as networks composed by distinctlayers, interacting and depending on each others. For example, in biology, agood description of the full protein-protein interactome requires, for someorganisms, up to seven distinct network layers, with thousands ofprotein-protein interactions each. A fundamental open question is then how muchinformation is really necessary to accurately represent the structure of amultilayer complex system, and if and when some of the layers can indeed beaggregated. Here we introduce a method, based on information theory, to reducethe number of layers in multilayer networks, while minimizing information loss.We validate our approach on a set of synthetic benchmarks, and prove itsapplicability to an extended data set of protein-genetic interactions, showingcases where a strong reduction is possible and cases where it is not. Usingthis method we can describe complex systems with an optimal trade--off betweenaccuracy and complexity.

Layer aggregation and reducibility of multilayer interconnected networks