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The goal of graphonmix is to generate\((U,W)\)-mixture graphs. These graphs aregenerated from a standard dense graphon\(W\) and a disjoint clique graphon\(U\), which acts as the sparse graphon. Moredetails can be found at (Kandanaarachchi and Ong 2025).

Installation

You can install the development version of graphonmix fromGitHub with:

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

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) = 0.1W<-matrix(0.1,nrow =100,ncol =100)# create the sparse part - a disjoint set of starswts<-c(0.5,0.3,0.2)# single function to generate a graph mixturegr1<-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 edgesvertex.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 plotgrdense<-sample_graphon(W,100)plot(grdense,edge.curved =0.3,vertex.size =degree(grdense)*0.1,edge.color ="lightgray",# Light colored edgesvertex.label =NA,vertex.color ="lightblue",main ="Dense Part")

# sample the sparse part and plotgrsparse<-generate_star_union(wts,300)plot(grsparse,edge.curved =0.3,vertex.size =degree(grsparse)*0.1,edge.color ="lightgray",# Light colored edgesvertex.label =NA,vertex.color ="lightblue",main ="Sparse Part")

# join the two graphs and plotgr2<-graph_join(grdense, grsparse,option =2)plot(gr2,edge.curved =0.3,vertex.size =degree(gr2)*0.1,edge.color ="lightgray",# Light colored edgesvertex.label =NA,vertex.color ="lightblue",main ="(U,W) Graph mixture")

Acknowledgements

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

References

Kandanaarachchi, Sevvandi, and Cheng Soon Ong. 2025. “Graphon Mixtures.”arXiv Preprint arXiv:2505.13864.

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