page_title: Rich-club coefficient
section_title: Assortativity
hierarchical_section_title: Rich-club coefficient / Related metrics / Assortativity
caption_attribution_description: English: An example of a network which is both disassortative and demostrates the Rich Club effect. The red nodes are hubs and form the "Rich Club."
context_page_description: The rich-club coefficient is a metric on graphs and networks, designed to measure the extent to which well-connected nodes also connect to each other. Networks which have a relatively high rich-club coefficient are said to demonstrate the rich-club effect and will have many connections between nodes of high degree. The rich-club coefficient was first introduced in 2004 in a paper studying Internet topology.
  This effect has been measured and noted on scientific collaboration networks and air transportation networks. It has been shown to be significantly lacking on protein interaction networks.
context_section_description: The Assortativity of a network is a measurement of how connected similar nodes are, where similarity is typically viewed in terms of node degree. Rich-club can be viewed as a more specific notation of assortativity, where we are only concerned with the connectivity of nodes beyond a certain richness metric. For example, if a network consisted of a collection of hub and spokes, where the hubs were well connected, such a network would be considered disassortative. However, due to the strong connectedness of the hubs in the network, the network would demonstrate the rich-club effect.
caption: An example of a network which is both disassortative and demonstrates the Rich Club effect. The red nodes are hubs and form the "Rich Club."
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