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 unnormalized measure proposed that there is somewhat difficult to interpret as it is not independent from the rich-club degree K, or, more precisely, it is negatively related to the number of nodes included in the rich-club pool (see Supplementary Fig. 1). The conventional correction for this dependency involves normalizing raw rich-club indices by richclub indices derived from randomly generated networks (Opsahl et al. 2008; Allstott et al. 2014). However, this correction may be undesirable in between-group analyses, because rich-club indices derived from randomly generated networks may also differ between groups (see Results below and Discussion). "
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    • "The centrality measures are well known for the unweighted graphs (Scott and Carrington, 2003; Wasserman and Faust, 1994) and some of them have been also extended to weighted systems (Barrat et al., 2004b; Opsahl et al., 2008). In the following, we survey the most relevant weighted measures and provide some hypotheses in order to capture the relationship between them and the network innovation performance. "
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