The conundrum of functional brain networks: small-world efficiency or fractal modularity

TL;DR

This paper explores the hierarchical organization of the human brain's functional networks, revealing a coexistence of fractal modularity and small-world efficiency, and emphasizes the importance of network science tools like percolation theory.

Contribution

It demonstrates how functional brain modules exhibit fractal structures and transition to small-world topology as weaker ties are included, advancing understanding of brain network organization.

Findings

Functional modules have fractal, self-similar topology.

Including weaker ties induces small-world properties.

Percolation theory highlights the modular character of brain networks.

Abstract

The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs.