Detecting rich-club ordering in complex networks

By Vittoria Colizza, Alessandro Flammini, M. Ángeles Serrano, Alessandro Vespignani. 2006

933 citations recorded by the source corpus.

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue in understanding their fabric and dynamical properties1,2,3,4,5. The ‘rich-club’ phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities, and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences4,5,6,7,8. Here, we provide the analytical expression and the correct null models that allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c65312eefd3a002029990cd22c3efc0b54325af1

How researchers see this paper

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

In Molecular Biology

In Statistical and Nonlinear Physics

Citations in the corpus

Graph theory methods: applications in brain networks (2018, neutral): “networks.”
Task-Based Core-Periphery Organization of Human Brain Dynamics (2012, background): “The RCC has also been extended to weighted networks [38], but it still requires one to specify a threshold value of richness to enable one to ask whether ‘‘rich’’ nodes tend to connect to other ‘‘rich’’ nodes.”
Structure and function of complex brain networks (2013, background): “pointed to the existence of a “rich club,” a set of hub regions that are more densely interconnected than predicted by chance alone.(67) Rich clubs may be significant features of network architecture as they provide a structural substrate for integrating and disseminating information across the enti”
Critical phenomena in complex networks (2007, background): “In a scale-free network, hubs may form a highly connected cluster (the rich-club phenomenon (Colizza et al., 2006; Zhou and Mondragón, 2004)).”
High-cost, high-capacity backbone for global brain communication (2012, background): “Φ(k) was normalized relative to the rich club coefficient Φrandom of a set of comparable random networks (n = 10,000) of equal size and degree sequence, giving a normalized rich club coefficient Φnorm (12) (SI Materials and Methods).”
Network hubs in the human brain. (2013, background): “Such collectives of high-degree nodes and their intercon-necting edges are referred to as a ‘rich club’ [46], a network attribute that tends to further boost the inﬂuence of its members by facilitating their mutual interactions.”
The science of science: from the perspective of complex systems (2017, background): “focused on the highly connected nodes in the collaboration network and revealed the ‘‘rich-club’’ phenomenon [66].”
Vital nodes identification in complex networks (2016, methodology): “However, this method could be inefficient since the nodes of the highest degrees (or other centrality measures) may be highly clustered as indicated by the rich-club phenomenon [183, 184], so that to target all of them is unnecessary.”