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


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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    • "are more strongly connected to each other than one would expect by chance alone — they form a rich club. We used a weighted rich club measure to calculate richness as a function of node strength (Opsahl et al., 2008 "
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    • "First, the weighted rich club coefficient Φ w (k) was computed as Φ w ðkÞ ¼ W Nk =∑ E Nk l¼1 w ranked l where the number of connections (E Nk ) and the sum of weights (W Nk ) were represented for nodal degrees (= the number of connections at a node) larger than k, and all nonzero elements of connectivity matrix were sorted by their weights, giving a vector of w l ranked . For comparison across individuals, Φ w (k) was typically normalized by the averaged values from 1000 random networks preserving the network size, weights, and degree distribution, giving the normalized rich club coefficient Φ n w (k) (Opsahl et al., 2008). As a function of degree k, rich club regime was defined if Φ n w is significant in N75% individuals for children (van den Heuvel and Sporns, 2011; van den Heuvel et al., 2013). "

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