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

The human brain has been studied at multiple scales, from neurons, circuits,areas with well defined anatomical and functional boundaries, to large-scalefunctional networks which mediate coherent cognition. In a recent work,we addressed the problem of the hierarchical organization in the brainthrough network analysis. Our analysis identified functional brainmodules of fractal structure that were inter-connected in a small-worldtopology. Here, we provide more details on the use ofnetwork science tools to elaborate on this behavior.We indicate the importance of using percolation theory to highlightthe modular character of the functional brain network.These modules present a fractal, self-similar topology, identified throughfractal 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 withminimal wiring costs