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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, weaddressed the problem of the hierarchical organization in the brain throughnetwork analysis. Our analysis identified functional brain modules of fractalstructure that were inter-connected in a small-world topology. Here, we providemore details on the use of network science tools to elaborate on this behavior.We indicate the importance of using percolation theory to highlight the modularcharacter of the functional brain network. These modules present a fractal,self-similar topology, identified through fractal network methods. When welower the threshold of correlations to include weaker ties, the network as awhole assumes a small-world character. These weak ties are organized preciselyas predicted by theory maximizing information transfer with minimal wiringcosts.

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