Article: Prominence and control: The weighted rich-club effect

December 12, 2008 at 12:00 am 4 comments

A paper called Prominence and control: The weighted rich-club effect that I have co-authored with Vittoria Colizza, Pietro Panzarasa, and José Javier Ramasco was published in the October 17 issue of Physical Review Letters (PRL). A pdf version of the paper is available.


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 the 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.

UPDATE: I have suggested an additional null model in Weighted Rich-club Effect: A more appropriate null model for scientific collaboration networks.

Want to test it with your data?

See the Weighted Rich-club Effect in the tnet manual.

If you use any of the information in this post, please cite: Opsahl, T., Opsahl, Colizza, V., Panzarasa, P., Ramasco, J.J., 2008. Prominence and control: The weighted rich-club effect. Physical Review Letters 101 (168702)

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Network? Weighted network? Local weighted rich-club measure

4 Comments Add your own

  • 1. Moitrayee  |  April 21, 2010 at 7:11 pm

    I was trying to use weighted_richclub_w .
    I am a little confused as to what are x,y,l99,l95,h99,h95.
    It would be great if you please help me out in understanding these parameters

  • 2. Moitrayee  |  April 21, 2010 at 7:56 pm

    The manual says it returns a table of phi(obs)/phi(null) which is equal to row(weighted). But the output table has six columns. So which column is the fraction here?
    I am a little confused and would greatly appreciate your help.

    • 3. Moitrayee Bhattacharyya  |  May 1, 2010 at 7:32 pm

      thanks a lot for your detailed reply. It was of great help.

  • 4. Tore Opsahl  |  April 23, 2010 at 11:52 am

    The output of the weighted_richclub_w-function is what you need to plot the diagrams in the paper – with some new features:
    – x: prominence parameter (horizonal axis, e.g., degree or strength)
    – y: observed phi over random phi-ratio (vertical axis)
    – l99, l95, h95, h99: the low and high 95% and 99% confidence intervals values from the distribution of the random phi. These values are divided by the average random phi to make them comparable to the ratio (y). See the blog post on the new randomisation procedure for two-mode networks for more info on the use of these values.


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