Today I read a paper titled “A small-world of weak ties provides optimal global integration of self-similar modules in functional brain networks”
The abstract is:
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.