Linking module properties to emergent behavior in composite networks

Determine a quantitative relationship that links the properties of primitive network components to the emergent behavior of composite networks (networks of networks), establishing how component-level characteristics translate into collective dynamics and macroscopic regimes.

Background

The paper studies how modular composition affects network dimensionality, showing that spectral and Fiedler dimensions can decouple in bundled and hierarchical network-of-networks architectures. While the authors develop analytical and renormalization-group tools to characterize emergent dimensions, they emphasize that connecting the properties of individual modules to global network behavior is a broader unresolved issue.

This open challenge spans biological, technological, and synthetic systems where complex architectures arise through tinkering and modular reuse. A rigorous link would clarify how local structural features govern diffusion, synchronization, and transport at macroscopic scales.