A small-world of weak ties provides optimal global integration of self-similar modules in functional brain networks

TL;DR

This paper proposes that weak ties in brain networks create a small-world architecture that balances modular independence with efficient global integration, revealing a natural solution to the brain's information transfer paradox.

Contribution

It introduces a hierarchical modular organization model showing how weak ties transform large-world modules into small-world networks, aligning with social network theories.

Findings

Weak ties organize as predicted by the theory to maximize information transfer.

Modules are large-world and self-similar, not small-world by themselves.

Incorporating weak ties results in a small-world network with optimal global integration.

Abstract

The human brain is organized in functional modules. Such an organization presents a basic 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 of short lengths and large local clustering may solve this problem. However, there is intrinsic tension between shortcuts generating small-worlds and the persistence of modularity; a global property unrelated to local clustering. Here, we present a possible solution to this puzzle. We first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks. These modules are "large-world" self-similar structures and, therefore, are far from being small-world. However, incorporating weaker ties to the network converts it into a small-world preserving an underlying backbone of well-defined modules. Remarkably, weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost. This trade-off architecture is reminiscent of the "strength of weak ties" crucial concept of social networks. Such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain.