brainGraph (version 1.0.0)

rich_club_norm: Calculate the normalized rich club coefficient

Description

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).

Usage

rich_club_norm(g, N = 100, rand = NULL, ...)

Arguments

g

An igraph graph object

N

Integer; the number of random graphs to generate (default: 100)

rand

A list of igraph graph objects, if random graphs have already been generated (default: NULL)

...

Other parameters (passed to rich_club_coeff)

Value

A list with four elements:

phi.rand

A matrix with N rows and max(degree(g)) columns, where each row contains the coefficients for a given random graph.

phi.orig

A vector of the rich-club coefficients for the original graph.

phi.norm

A named vector of the normalized rich club coefficients.

p

The p-value based on the N random graphs generated.

References

Colizza V., Flammini A., Serrano M.A., Vespignani A. (2006) Detecting rich-club ordering in complex networks. Nature Physics, 2:110-115.

See Also

sim.rand.graph.par Other Rich-club functions: plot_rich_norm, rich_club_attrs, rich_club_coeff, rich_core