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graphonmix

The goal of graphonmix is to generate dense or sparse graphs via different techniques. We explore \((U,W)\)-mixture graphs and graphettes. \((U,W)\)-mixture graphs are generated from a standard dense graphon \(W\) and a disjoint clique graphon \(U\), which acts as the sparse graph generator. Graphettes are a triple consisting of a graphon \(W\), a sparsifing sequence \(\{\rho_n\}_n\) with \(\rho_n \to 0\) and graph edit function \(f\). \((U,W)\)-mixture graphs are discussed in (Kandanaarachchi and Ong 2026) and graphettes are discussed in (Wijesinghe et al. 2026).

Installation

You can install the development version of graphonmix from GitHub with:

# install.packages("pak")
pak::pak("sevvandi/graphonmix")

\((U,W)\) Mixture Example

This is a basic example on how to sample a \((U,W)\)-mixture graph.

library(graphonmix)
library(igraph)
#> 
#> Attaching package: 'igraph'
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union
# create the dense graphon W(x,y) = 0.1
W <- matrix(0.1, nrow = 100, ncol = 100)
# create the sparse part - a disjoint set of stars
wts <- c(0.5, 0.3, 0.2)
# single function to generate a graph mixture
gr1 <- sample_mixed_graph(W, wts, nd = 100, ns = 300, p = 0.5, option = 2)
plot(gr1,
     edge.curved = 0.3,
     vertex.size = degree(gr1)*0.1,
     edge.color = "lightgray",     # Light colored edges
     vertex.label = NA,
     vertex.color = "lightblue",
     main = "(U,W) Graph mixture"
)

Graphette example

This is an example with \(\rho_n = 10/n\) and \(f = \text{star_f1}\). The graph edit function \(\text{star_f1}\) adds stars using a Poisson process.

rho <- function(n) 20/n
gr <- sample_graphette(W, 
                       rho_n = rho, 
                       graph_edit_f = 'star_f1',
                       n = 200,
                       t_or_p = 2)

plot(gr, vertex.label = NA, vertex.size = 3)

Acknowledgements

A big thank you to Sashenka Fernando for helping me with the hex sticker.

References

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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