Article

Prominence and Control: The Weighted Rich-Club Effect

School of Business and Management, Queen Mary College, University of London, London, United Kingdom.
Physical Review Letters (Impact Factor: 7.51). 11/2008; 101(16):168702. DOI: 10.1103/PhysRevLett.101.168702
Source: PubMed

ABSTRACT Complex systems are often characterized by large-scale hierarchical organizations. Whether the prominent elements, at the top of the hierarchy, share and control resources or avoid one another lies at the heart of a system's global organization and functioning. Inspired by network perspectives, we propose a new general framework for studying the tendency of prominent elements to form clubs with exclusive control over the majority of a system's resources. We explore associations between prominence and control in the fields of transportation, scientific collaboration, and online communication.

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    • "The brain's rich-club has been described previously (Collin et al., 2013; van den Heuvel et al., 2012; van den Heuvel and Sporns, 2011). For the weighted networks, the rich-club coefficient (RC) / w ðkÞ is given by (Opsahl et al., 2008): "
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    ABSTRACT: Lifespan is a dynamic process with remarkable changes in brain structure and function. Previous neuroimaging studies have indicated age-related microstructural changes in specific white matter tracts during development and aging. However, the age-related alterations in the topological architecture of the white matter structural connectome across the human lifespan remain largely unknown. Here, a cohort of 113 healthy individuals (ages 9-85) with both diffusion and structural MRI acquisitions were examined. For each participant, the high-resolution white matter structural networks were constructed by deterministic fiber tractography among 1024 parcellation units and were quantified with graph theoretical analyses. The global network properties, including network strength, cost, topological efficiency, and robustness, followed an inverted U-shaped trajectory with a peak age around the third decade. The brain areas with the most significantly nonlinear changes were located in the prefrontal and temporal cortices. Different brain regions exhibited heterogeneous trajectories: the posterior cingulate and lateral temporal cortices displayed prolonged maturation/degeneration compared with the prefrontal cortices. Rich-club organization was evident across the lifespan, whereas hub integration decreased linearly with age, especially accompanied by the loss of frontal hubs and their connections. Additionally, age-related changes in structural connections were predominantly located within and between the prefrontal and temporal modules. Finally, based on the graph metrics of structural connectome, accurate predictions of individual age were obtained (r = 0.77). Together, the data indicated a dynamic topological organization of the brain structural connectome across human lifespan, which may provide possible structural substrates underlying functional and cognitive changes with age. Hum Brain Mapp, 2015. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.
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    • "Additionally , the ϕ w (k) is normalized to the averaged ϕ w (k) of a 1000 random networks with equal density and degree distribution. Normalized values of >1 over a range of k levels define the presence of rich club organization (Opsahl et al., 2008), indicating that nodes with higher degrees tend to be interconnected by stronger edges than would be predicted by chance. For subsequent analyses, the top 10 (15%) nodes in group-averaged node degree were considered to be part of the rich club (Collin, Kahn, de Reus, Cahn, & van den Heuvel, 2014; Van den Heuvel et al., 2013). "
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    ABSTRACT: The human brain is a complex network that has been noted to contain a group of densely interconnected hub regions. With a putative "rich club" of hubs hypothesized to play a central role in global integrative brain functioning, we assessed whether hub and rich club organizations are associated with cognitive performance in healthy participants and whether the rich club might be differentially involved in cognitive functions with a heavier dependence on global integration. A group of 30 relatively older participants (range = 40-79 years of age) underwent extensive neuropsychological testing, combined with diffusion-weighted magnetic resonance imaging to reconstruct individual structural brain networks. Rich club connectivity was found to be associated with general cognitive performance. More specifically, assessing the relationship between the rich club and performance in two specific cognitive domains, we found rich club connectivity to be differentially associated with attention/executive functions-known to rely on the integration of distributed brain areas-rather than with visuospatial/visuoperceptual functions, which have a more constrained neuroanatomical substrate. Our findings thus provide first empirical evidence of a relevant role played by the rich club in cognitive processes.
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    • "However, the value is sensitive to the overall number of links and nodes which makes it difficult to define what 'high' and 'low' values mean exactly. Defining the benchmark value, we create 1000 random networks with the same properties (number of nodes, links, weights) as those of the observed network by reshuffling the links among nodes (Opsahl et al. 2008). The benchmark value is the mean value of the 1000 random networks, but an observed value is deemed significantly high or low if it deviates from the mean value of the 1000 random networks by at least 2 standard deviations. "
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