Unveiling the Dimensionality of Networks of Networks

"Every object that biology studies is a system of systems." (Fran\c{c}ois Jacob, 1974). Most networks feature intricate architectures originating from tinkering, a repetitive use of existing components where structures are not invented but reshaped. Still, linking the properties of primitive components to the emergent behavior of composite networks remains a key open challenge. Here, by composing scale-invariant networks, we show how tinkering decouples Fiedler and spectral dimensions, hitherto considered identical, providing valuable insights into mesoscopic and macroscopic collective regimes.