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

The human brain is organized in functional modules. Such an organization poses a conundrum: modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture may solve this problem. However, there is intrinsic tension between shortcuts generating small-worlds and the persistence of modules. Here we provide a solution to this puzzle. We show that the functional brain network formed by percolation of strong links is highly modular. Contrary to the common view, modules are self-similar and therefore are very far from being small-world. Incorporating the weak ties to the network converts it into a small-world preserving an underlying backbone of well-defined modules. Weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs. This tradeoff architecture is reminiscent of the “strength of weak ties” crucial concept of social networks and provides a natural solution to the puzzle of efficient information flow in the highly modular structure of the brain.