From Sociology to Neuroscience: the strength of weak links

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, at the same time, sufficiently connected to bind multiple processors for efficient information transfer in the whole brain. How is this solved? Here we show a formal solution to this problem is the formation of two networks. A skeleton of strong links forms a highly modular and fragmented structure. This network is embedded in a sea of weak links which optimally (achieving maximal connectivity per unit of wire) binds these modules together. This proposal is inspired by a fundamental notion of sociology termed "the strength of weak ties" (Ref 2). According to this theory, strong ties (close friends) clump together forming modules. An acquaintance (weak tie) becomes a crucial bridge (a shortcut) between the two densely knit clumps (modules) of close friends.

HFSP Career Development Award and Program Grant holder Mariano Sigman and colleagues
authored on Wed, 29 February 2012

We analyzed the topology of brain connectivity using a method of statistical physics known as percolation. Percolation can be visualized as water flow in a network of pipes. A "pipe" in our brain network (a link between two voxels) is added when two voxels have similar temporal patterns which indicates that they fluctuate coherently. As the degree of similarity required to include a link is lowered, the density of pipes in the network increases and more voxels become connected.  A fundamental result of statistical physics is that in uncorrelated networks there is a critical value in which there is a phase transition in which the network gets fully connected. 

Instead, the functional brain networks analyzed here showed, as the threshold of similarity is lowered, a series of discrete transitions. Each transition reflects that with the inclusion of a new link, two modules of the network which were not connected at higher threshold were linked. This shortcut which brings together different neighborhoods of the brain is a weak link. Hence, as in sociology, the weak links end up being the most relevant ones because they bring together the network globally.

A very original aspect of our investigation is that we could show that the distribution of weak links was exactly as predicted by theory to optimize the compactness of the network using the minimal amount of wire. This is not a fit of a parameter. Instead, it is a full quantitative prediction of the density of weak links which was observed in the data. Bringing theory to neuroscience was an interesting aspect of this investigation.



1. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. Lazaros K. Gallos, Hernán A. Makse, and Mariano Sigman. PNAS 2012 109 (8) 2825-2830; published ahead of print February 3, 2012, doi:10.1073/pnas.1106612109.

Other References

2. The strength of weak ties.  Granovetter MS.  (1973)  Am J Socio l78:1360–138.

Pubmed link