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The goal of graphonmix is to generate \((U,W)\)-mixture graphs. These graphs are generated from a standard dense graphon \(W\) and a disjoint clique graphon \(U\), which acts as the sparse graphon. More details can be found at (Kandanaarachchi and Ong 2025).
You can install the development version of graphonmix from GitHub with:
# install.packages("pak")
pak::pak("sevvandi/graphonmix")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"
)
Or you can generate the two graphs separately and join them.
# sample the dense part and plot
grdense <- sample_graphon(W, 100)
plot(grdense,
edge.curved = 0.3,
vertex.size = degree(grdense)*0.1,
edge.color = "lightgray", # Light colored edges
vertex.label = NA,
vertex.color = "lightblue",
main = "Dense Part"
)
# sample the sparse part and plot
grsparse <- generate_star_union(wts, 300)
plot(grsparse,
edge.curved = 0.3,
vertex.size = degree(grsparse)*0.1,
edge.color = "lightgray", # Light colored edges
vertex.label = NA,
vertex.color = "lightblue",
main = "Sparse Part"
)
# join the two graphs and plot
gr2 <- graph_join(grdense, grsparse, option = 2)
plot(gr2,
edge.curved = 0.3,
vertex.size = degree(gr2)*0.1,
edge.color = "lightgray", # Light colored edges
vertex.label = NA,
vertex.color = "lightblue",
main = "(U,W) Graph mixture"
)
A big thank you to Sashenka Fernando for helping me with the hex sticker.
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.