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

By Lazaros K. Gallos, Hernán A. Makse, Mariano Sigman. Proceedings of the National Academy of Sciences of the United States of America, 2011

381 citations recorded by the source corpus.

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.

Subfields: Cognitive Neuroscience, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3bf478c46f742428f4e74cacdaddf77e42cd6fde

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cognitive Neuroscience

In Statistical and Nonlinear Physics

Citations in the corpus

Growing Homophilic Networks Are Natural Navigable Small Worlds (2015, positive): “Power law link length distributions with α = d + 1 are encountered in real-life networks like airport connections networks[52] and functional brain networks[53, 54].”
Griffiths phases and the stretching of criticality in brain networks (2013, methodology): “[37], who found that (functional) brain networks consist of a myriad of densely connected local moduli, which altogether form a large world structure and, therefore, are far from being smallworld; however, incorporating weak ties into the network converts it into a small world preserving an underlyi”
Modular Brain Networks (2015, background): “…pathways, modularity has been shown to promote specialization (Espinosa-Soto & Wagner 2010), and it has been suggested that the persistence of modular organization cross-linked by long-distance weak ties is crucial for preserving functional specialization in brain networks (Gallos et al. 2012).”
Proportional thresholding in resting‐state fMRI functional connectivity networks and consequences for patient‐control connectome studies: Issues and recommendations (2017, positive): “Although studies have suggested that this operation may ignore potentially valuable information during functional network construction (Gallos et al., 2012; Goulas et al., 2015; Santarnecchi et al., 2014), thresholding is a commonly applied approach in functional connectomics to remove spurious conn”
Structural and Functional Brain Networks: From Connections to Cognition (2013, background): “It is also potentially blind to weak long-range axonal connections, which may serve as weak ties for global integration (11, 12).”
Communication dynamics in complex brain networks (2017, background): “A high within-module connection density promotes high within-module communication efficiency 87 ; sparser connections between modules enable efficient inter-module integration of information 28,88,89 .”
Avoiding catastrophic failure in correlated networks of networks (2014, background): “LETTERS PUBLISHED ONLINE: 14 SEPTEMBER 2014 | DOI: 10.1038/NPHYS3081 Avoiding catastrophic failure in correlated networks of networks”
Diaschisis: past, present, future. (2014, background): “This is particularly important in the study of long-range connections responsible for integration between remote brain regions (Gallos et al., 2012).”
Identifying influential spreaders in complex networks based on gravity formula (2015, background): “t networks in nature do not act in isolation, but instead exchange information and depend on one another to function properly, that is to say, natural systems are organized in interconnected networks [40,41,42]; And some real spreading dynamics like the diﬀusion of rumors or opinions, the rise of sc”