rich_club: Rich club calculations

Description Usage Arguments Details Value Author(s) References See Also

Description

rich_club_coeff calculates the rich club of a graph, returning the rich-club coefficient, φ, and the subgraph of rich club vertices.

rich_club_norm will (optionally) generate a number of random graphs, calculate their rich club coefficients (φ), and return φ_{norm} of the graph of interest, which is the observed rich-club coefficient divided by the mean across the random graphs.

rich_core finds the boundary of the rich core of a graph, based on the decreasing order of vertex degree. It also calculates the degree that corresponds to that rank, and the core size relative to the total number of vertices in the graph.

Usage

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rich_club_coeff(g, k = 1, weighted = FALSE)

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

rich_core(g)

Arguments

g

An igraph graph object

k

Integer; the minimum degree for including a vertex (default: 1)

weighted

Logical indicating whether or not edge weights should be used (default: FALSE)

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 sim.rand.graph.par)

Details

If random graphs have already been generated, you can supply a list as an argument (since graph generation is time consuming).

Value

rich_club_coeff - a list with components:

phi

The rich club coefficient, φ.

graph

A subgraph containing only the rich club vertices.

Nk

The number of vertices in the rich club graph.

Ek

The number of edges in the rich club graph.

rich_club_norm - a data table with columns:

k

Sequence of degrees

rand

Rich-club coefficients for the random graphs

orig

Rich-club coefficients for the original graph.

norm

Normalized rich-club coefficients.

p

The P-values based on the distribution of rich-club coefficients from the random graphs.

p.fdr

The FDR-adjusted P-values

density

The observed graph's density

threshold
Group
name

rich_core - a data frame with columns:

density

The density of the graph.

rank

The rank of the boundary for the rich core.

k.r

The degree of the vertex at the boundary.

core.size

The size of the core relative to the graph size.

Author(s)

Christopher G. Watson, [email protected]

References

Zhou S., Mondragon R.J. (2004) The rich-club phenomenon in the internet topology. IEEE Comm Lett, 8:180-182.

Opsahl T., Colizza V., Panzarasa P., Ramasco J.J. (2008) Prominence and control: the weighted rich-club effect. Physical Review Letters, 101.16:168702.

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

Ma A & Mondragon R.J. (2015) Rich-cores in networks. PLoS One, 10(3): e0119678. doi: 10.1371/journal.pone.0119678

See Also

Other Rich-club functions: plot_rich_norm, rich_club_attrs

Other Random graph functions: RandomGraphs, analysis_random_graphs


brainGraph documentation built on May 29, 2018, 9:03 a.m.