title: A unifying framework for measuring weighted rich clubs.
abstract: Network analysis can help uncover meaningful regularities in the organization of complex systems. Among these, rich clubs are a functionally important property of a variety of social, technological and biological networks. Rich clubs emerge when nodes that are somehow prominent or 'rich' (e.g., highly connected) interact preferentially with one another. The identification of rich clubs is non-trivial, especially in weighted networks, and to this end multiple distinct metrics have been proposed. Here we describe a unifying framework for detecting rich clubs which intuitively generalizes various metrics into a single integrated method. This generalization rests upon the explicit incorporation of randomized control networks into the measurement process. We apply this framework to real-life examples, and show that, depending on the selection of randomized controls, different kinds of rich-club structures can be detected, such as topological and weighted rich clubs.
authors.affiliation: 1] Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ UK [2] Section on Critical Brain Dynamics, National Institute of Mental Health, Bethesda, 20892 Maryland, USA.
authors.forename: Jeff
authors.initials: J
authors.lastname: Alstott
authors.affiliation: School of Business and Management, Queen Mary University of London, London, E1 4NS UK.
authors.forename: Pietro
authors.initials: P
authors.lastname: Panzarasa
authors.affiliation: 1] Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ UK [2] Churchill College, University of Cambridge, Cambridge CB2 0SZ UK.
authors.forename: Mikail
authors.initials: M
authors.lastname: Rubinov
authors.affiliation: Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ UK.
authors.forename: Edward T
authors.initials: ET
authors.lastname: Bullmore
authors.affiliation: Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ UK.
authors.forename: Petra E
authors.initials: PE
authors.lastname: Vértes
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D010363:Pattern Recognition, Automated / Q000379:methods*; D060756:Social Networking