Generates Dense and Sparse Graphs using Graphon Extensions

Generates dense or sparse graphs using graphon mixtures and graphettes. Graphon mixtures uses two graphons U and W to generate graphs. Sparse graphs are generated in this case using the inverse line graph (root) operation. Graphettes have 3 components, the graphon W, a real-valued sequence and a graph edit function. Both techniques can generate dense or sparse graphs. Kandanaarachchi and Ong (2026) , Wijesinghe et al (2026) .

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