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

Levich Institute and Physics Department, City College of New York, New York, NY 10031, USA.
Proceedings of the National Academy of Sciences (Impact Factor: 9.67). 02/2012; 109(8):2825-30. DOI: 10.1073/pnas.1106612109
Source: PubMed


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.

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    • "This is in agreement with the conjecture that finite dimensionality is required for the existence of GPs [3]. Moreover, many real networks, as for instance brain connectomes, have a modular organization, where modules are finite, heterogeneous and weakly connected [39]. Slow dynamics has been reported in models defined on hierarchical modular networks [4] [14] [40]. "
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