Structural reducibility of multilayer networks

TLDR

Complex systems are often modeled as multilayer networks, where each layer captures distinct interaction types, such as the multi‑layer protein‑protein interactome in biology that may involve up to seven layers. The study seeks to determine when and how layers in a multilayer network can be aggregated without losing essential structural information. We propose an information‑theoretic reduction method, validated on synthetic benchmarks and protein‑genetic interaction data, that identifies which layers can be merged while preserving network structure. The method achieves an optimal trade‑off between accuracy and complexity, demonstrating that substantial layer reduction is possible in some systems but not in others.

Abstract

Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, with thousands of protein-protein interactions each. A fundamental open question is then how much information is really necessary to accurately represent the structure of a multilayer complex system, and if and when some of the layers can indeed be aggregated. Here we introduce a method, based on information theory, to reduce the number of layers in multilayer networks, while minimizing information loss. We validate our approach on a set of synthetic benchmarks, and prove its applicability to an extended data set of protein-genetic interactions, showing cases where a strong reduction is possible and cases where it is not. Using this method we can describe complex systems with an optimal trade--off between accuracy and complexity.