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

2011/02/28 by Lazaros K. Gallos, Hernán A. Makse, Hernan A. Makse +1 · 425 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Architecture #Biology #Complex Network Analysis Techniques #Computer science #Distributed computing #Functional Brain Connectivity Studies #Information transfer #Mathematics #Modular design #Modularity (biology) #Neural dynamics and brain function #Neuroscience #Parallel computing #Percolation (cognitive psychology) #Property (philosophy) #Set (abstract data type) #Theoretical computer science #Topology (electrical circuits) #Transfer (computing) #cond-mat.stat-mech #cs.SI #physics.bio-ph #physics.soc-ph #q-bio.NC

paper · pdf · doi:10.1073/pnas.1106612109

published in Proceedings of the National Academy of Sciences 109(8), 2825-2830 (National Academy of Sciences) · 37 pages, 11 figures

openalex publication_date 2012/02/03 · arxiv created 2012/05/11 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 paths 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.

Citations

• Scaling theory of transport in complex biological networks

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