This function will (optionally) generate a number of random graphs, calculate their rich club coefficients (\(\phi\)), and return \(\phi\) of the graph of interest divided by the mean across random graphs, i.e. \(\phi_{norm}\). If random graphs have already been generated, you can supply a list as an argument (since graph generation is time consuming).
rich_club_norm(g, N = 100, rand = NULL, ...)An igraph graph object
Integer; the number of random graphs to generate (default: 100)
A list of igraph graph objects, if random graphs have
already been generated (default: NULL)
Other parameters (passed to sim.rand.graph.par)
A data table with columns:
Sequence of degrees
Rich-club coefficients for the random graphs
Rich-club coefficients for the original graph.
Normalized rich-club coefficients.
The P-values based on the distribution of rich-club coefficients from the random graphs.
The FDR-adjusted P-values
The observed graph's density
(if applicable)
Colizza V., Flammini A., Serrano M.A., Vespignani A. (2006) Detecting rich-club ordering in complex networks. Nature Physics, 2:110-115.
Other Rich-club functions: plot_rich_norm,
rich_club_attrs,
rich_club_coeff, rich_core
Other Random graph functions: RandomGraphs,
analysis_random_graphs