Description Usage Arguments Details Value Author(s) References See Also
rich_club_coeff
calculates the rich club of a graph, returning
the richclub 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 richclub
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.
1 2 3 4 5  rich_club_coeff(g, k = 1, weighted = FALSE)
rich_club_norm(g, N = 100, rand = NULL, ...)
rich_core(g)

g 
An 
k 
Integer; the minimum degree for including a vertex (default: 1) 
weighted 
Logical indicating whether or not edge weights should be
used (default: 
N 
Integer; the number of random graphs to generate (default: 100) 
rand 
A list of 
... 
Other parameters (passed to 
If random graphs have already been generated, you can supply a list as an argument (since graph generation is time consuming).
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 
Richclub coefficients for the random graphs 
orig 
Richclub coefficients for the original graph. 
norm 
Normalized richclub coefficients. 
p 
The Pvalues based on the distribution of richclub coefficients from the random graphs. 
p.fdr 
The FDRadjusted Pvalues 
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. 
Christopher G. Watson, [email protected]
Zhou S., Mondragon R.J. (2004) The richclub phenomenon in the internet topology. IEEE Comm Lett, 8:180182.
Opsahl T., Colizza V., Panzarasa P., Ramasco J.J. (2008) Prominence and control: the weighted richclub effect. Physical Review Letters, 101.16:168702.
Colizza V., Flammini A., Serrano M.A., Vespignani A. (2006) Detecting richclub ordering in complex networks. Nature Physics, 2:110115.
Ma A & Mondragon R.J. (2015) Richcores in networks. PLoS One, 10(3): e0119678. doi: 10.1371/journal.pone.0119678
Other Richclub functions: plot_rich_norm
,
rich_club_attrs
Other Random graph functions: RandomGraphs
,
analysis_random_graphs
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