Unveiling the Dimensionality of Networks of Networks

TL;DR

This paper investigates how the process of tinkering in network construction affects the spectral and Fiedler dimensions, revealing their decoupling and providing insights into the behavior of complex, multi-scale networks.

Contribution

It demonstrates that tinkering can decouple spectral and Fiedler dimensions in scale-invariant networks, offering new understanding of their emergent properties.

Findings

Decoupling of spectral and Fiedler dimensions due to tinkering

Insights into mesoscopic and macroscopic collective regimes

Analysis of scale-invariant network compositions

Abstract

"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.