Package {graphonmix}

Type: Package
Title: Generates Dense and Sparse Graphs using Graphon Extensions
Version: 0.1.1
Maintainer: Sevvandi Kandanaarachchi <sevvandik@gmail.com>
Description: 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) <doi:10.48550/arXiv.2505.13864>, Wijesinghe et al (2026) <doi:10.48550/arXiv.2602.23566>.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.3.3
Imports: ggplot2, igraph, imager, stats
Suggests: gridExtra, knitr, rmarkdown
VignetteBuilder: knitr
URL: https://sevvandi.github.io/graphonmix/
NeedsCompilation: no
Packaged: 2026-06-12 06:20:37 UTC; kan092
Author: Sevvandi Kandanaarachchi ORCID iD [aut, cre]
Repository: CRAN
Date/Publication: 2026-06-12 07:50:02 UTC

graphonmix: Generates Dense and Sparse Graphs using Graphon Extensions

Description

logo

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 sparsifying sequence and a graph edit function. Both techniques can generate dense or sparse graphs. Kandanaarachchi and Ong (2026) doi:10.48550/arXiv.2505.13864, Wijesinghe et al (2026) doi:10.48550/arXiv.2602.23566.

Author(s)

Maintainer: Sevvandi Kandanaarachchi sevvandik@gmail.com (ORCID)

See Also

Useful links:

Plots the output of extract_sparse function.

Description

Plots the two lines fitted to the unique, sorted log degrees of the graph.

Usage

## S3 method for class 'extract_sparse'
autoplot(object, ...)

Arguments

object

The output of the function 'extract_sparse'

...

Other arguments currently ignored

Value

A ggplot object.

Examples

library(igraph)
gr <- sample_pa(10000, power = 1.2, directed = FALSE)
sparse <- extract_sparse(gr)
autoplot(sparse)

Plots the output of separate_dense_and_sparse.

Description

Plots the three lines fitted to the unique, sorted log degrees of the graph.

Usage

## S3 method for class 'separate_dense_and_sparse'
autoplot(object, ...)

Arguments

object

The output of the function 'separate_dense_and_sparse.'

...

Other arguments currently ignored

Value

A ggplot object.

Examples

library(igraph)
W <- matrix(0.1, nrow = 100, ncol = 100)
wts <- c(0.5, 0.3, 0.2)
ns <- 200
nd <- 100
p <- 0.5
gr <- sample_mixed_graph(W, wts, nd, ns, p = 0.1, option = 2)
out <- separate_dense_and_sparse(gr)
separate <- separate_dense_and_sparse(gr)
autoplot(separate)

Creates an exponential graphon

Description

Creates an nxn matrix where the (i,j)th entry is exp(-(i+j)/scalar)

Usage

create_exp_matrix(nrow, scalar)

Arguments

nrow

The dimension of the matrix

scalar

The scalar in exp(-(i+j)/scalar)

Value

An nxn matrix

Examples

W <- create_exp_matrix(100, 100)

Computes empirical graphon from graph

Description

Computes empirical graphon given a graph

Usage

empirical_graphon(gr, n = NULL)

Arguments

gr

A graph

n

Dimension of the graphon matrix

Value

The empirical graphon

Examples

library(igraph)
gr <- sample_gnp(1000, p=0.2)
emp <-  empirical_graphon(gr, n = 100)

Extracts the sparse part from a (U,W) graphon mixture

Description

This function extracts the sparse component from a (U,W) mixture graph by fitting two lines to the unique sorted log degree values. The first line gives the number of hubs in the sparse part and the remaining line fits the degrees of the dense part.

Usage

extract_sparse(gr)

Arguments

gr

The input graph

Value

a list with the following components:

num_hubs

The number of hubs in the sparse component.

phat

The probability vector of the sparse component. This is also known as the mass partition.

segment_sizes

The sizes of the two line segments.

line_equations

The two equations of the lines.

cutoff

The best cut off for the two lines.

models

The models of the fitted lines.

mse

The mean squared error

data

The degree data.

Examples

library(igraph)
gr <- sample_pa(10000, power = 1.2, directed = FALSE)
sparse <- extract_sparse(gr)
sparse$phat

Generates a sparse graph of star graphs

Description

Generates a union of star graphs given the weights

Usage

generate_star_union(wts, n)

Arguments

wts

The proportion of the hub degrees

n

The number of nodes in the new graph

Value

A disjoint union of star graphs

Examples

library(igraph)
wts <- c(0.5, 0.3, 0.2)
gr <- generate_star_union(wts, n = 100)
gr

Joins two graphs

Description

Joins two graphs randomly connecting vertices

Usage

graph_join(gr1, gr2, p = 0.5, option = 2)

Arguments

gr1

The first graph to join

gr2

The second graph to join

p

The proportion of edges in gr1 to be added as part of the joining

option

Two options. 1 does the disjoint union, 2 does the random edges union.

Value

The joined graph

Examples

W <- create_exp_matrix(100, 100)
# create the sparse part - a disjoint set of stars
wts <- c(0.5, 0.3, 0.2)
grdense <- sample_graphon(W, 100)
grsparse <- generate_star_union(wts, 200)
gr <- graph_join(grdense, grsparse, opt = 2)

Creates a line graphon from a sequence of probabilities

Description

Creates a line graphon, which is a disjoint clique graphon from a sequence of probability values

Usage

line_graphon(probs)

Arguments

probs

The list of probabilities starting from the largest.

Value

The line graphon

Examples

library(ggplot2)
wts <- c(0.5, 0.3, 0.2)
U <- line_graphon(wts)
plot_graphon(U)

Plots graphon

Description

Plots graphon

Usage

plot_graphon(W, cols = c("white", "black"))

Arguments

W

A graphon given by an nxn matrix

cols

Colors, by default white and black

Value

A ggplot object.

Examples

W <- create_exp_matrix(100, 100)
plot_graphon(W)

Predicts the degree of hubs of an new graph

Description

Predicts the degree of hubs of an unseen graph given a graph generated from the same process.

Usage

predict_hubs(gr, n, k = NULL)

Arguments

gr

The input graph

n

The number of nodes in the new graph

k

The number of hubs. Default is NULL

Value

A vector of hub degrees

Examples

library(igraph)
gr <- sample_pa(10000, power = 1.2, directed = FALSE)
predict_hubs(gr, n = 11000)

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

ggplot2

autoplot

Creates a ring graphon

Description

Creates an graphon which can generate ring graphs.

Usage

ring_graphon(n, alpha = 0.1)

Arguments

n

The dimension of the matrix

alpha

A scaling factor used in the graphon. Default set to 0.1

Value

An nxn matrix

Examples

# example code
W <- ring_graphon(100)
plot_graphon(W)

Samples a graph from a graphette

Description

Samples a graph from a graphette given by (W, a_n, f), where W is the graphon, a_n is generally a sequence converging to zero and f is a graph edit funcion.

Usage

sample_graphette(
  W,
  rho_n = NULL,
  graph_edit_f = NULL,
  n = 100,
  t_or_p = 0.5,
  ring_sizes = c(5, 6)
)

Arguments

W

The graphon. This is a symmetric matrix with values in [0,1]

rho_n

A function. Default is 1.

graph_edit_f

The graph edit function. For star functions it can be one of 'star_f1', 'star_f2', 'star_f3', 'star_f4' or 'star_f5'. To add rings, it needs to be 'add_rings'. The function 'remove_cycles' removes cycles.

n

The number of nodes in the graph to sample

t_or_p

The parameter for star function or the ring function. For the ring function it needs to be between 0 and 1.

ring_sizes

The size of rings to add if the graph edit function is the ring function. default values set to c(5,6).

Value

gr A graph sampled from rho_n W.

Examples

library(igraph)
# Example 1
f1 <- function(n) 10/n
W <- matrix(0.2, nrow = 100, ncol = 100)
gr <- sample_graphette(W, rho_n = f1, graph_edit_f = 'add_rings', n = 100, t_or_p = 0.5)
gr

# Example 2
gr <- sample_graphette(W, rho_n = f1, graph_edit_f = 'star_f1', n = 100, t_or_p = 3)
gr

Generates a graph given a graphon

Description

Generates a graph given a dense graphon W.

Usage

sample_graphon(W, n)

Arguments

W

A graphon given by a matrix

n

The number of nodes of the sampled graph

Value

A graph sampled from the graphon W with n nodes

Examples

library(igraph)
W <- matrix(0.2, nrow = 100, ncol = 100)
gr <- sample_graphon(W, n= 100)

Generate a (U,W) mixture graph

Description

Generate a (U,W) mixture graph from a dense graphon W and a mass partition corresponding to a line graph graphon U.

Usage

sample_mixed_graph(W, wts, nd, ns, p = 0.5, option = 2)

Arguments

W

The dense graphon. This is a symmetric matrix with values in [0,1]

wts

The degree proportions of the hub degrees. Need to add up to 1. This is the mass partition corresponding to the line graph graphon U.

nd

The number of nodes in the dense part of the graph

ns

The number of nodes in the sparse part of the graph

p

The nodes to be added as a proportion of the edges in the dense part

option

Graph joining option. If option == 1 then a disjoit union is considered. If option == 2 the two graphs are joined randomly with the number of edges specified by p.

Value

A graph sampled from the (U,W) mixture.

Examples

library(igraph)
W <- matrix(0.1, nrow = 100, ncol = 100)
wts <- c(0.5, 0.3, 0.2)
ns <- 200
nd <- 100
p <- 0.5
gr <- sample_mixed_graph(W, wts, nd, ns, p, option = 2)
gr

Samples a graph from a sparsified graphon

Description

Samples a graph from a sparsified graphon given by a_n W, where W is the graphon and a_n is generally a sequence converging to zero.

Usage

sample_sparse_graphon(W, rho_n = NULL, n)

Arguments

W

The graphon. This is a symmetric matrix with values in [0,1]

rho_n

A function. Default is 1.

n

The number of nodes in the graph to sample

Value

gr A graph sampled from rho_n W.

Examples

library(igraph)
f1 <- function(n) 10/n
W <- matrix(0.2, nrow = 100, ncol = 100)
gr <- sample_sparse_graphon(W, f1, n = 100)
gr

Creates a Stochastic Block Model graphon

Description

Creates an graphon representing a Stochastic Block Model (SBM).

Usage

sbm_graphon(mat, n)

Arguments

mat

The matrix representing the SBM

n

The dimension of the matrix

Value

An nxn matrix

Examples

# example code
mat <- matrix(c(0.9, 0.01, 0.02,
0.01, 0.8, 0.03,
0.02, 0.03, 0.7), nrow = 3, byrow = TRUE)
W <- sbm_graphon(mat, 100)
plot_graphon(W)

Scales a graphon to an nxn matrix

Description

Scales a graphon to an nxn matrix suitable for large adjacency matrices

Usage

scale_graphon(W, n)

Arguments

W

A graphon given as a symmetric square matrix

n

The dimension of the output matrix

Value

Scaled nxn graphon

Examples

library(igraph)
gr <- sample_gnp(1000, p=0.2)
adj <- as_adjacency_matrix(gr)
W <- scale_graphon(adj, 100)

Separates the dense and sparse part from a (U,W) graphon mixture

Description

This function breaks a (U,W) mixture graph into a dense and sparse component.

Usage

separate_dense_and_sparse(grmix)

Arguments

grmix

The input graph

Value

a list with the following components:

gr_dense

The dense component.

gr_sparse

The sparse component.

data

The original graph.

Examples

library(igraph)
W <- matrix(0.1, nrow = 100, ncol = 100)
wts <- c(0.5, 0.3, 0.2)
ns <- 200
nd <- 100
p <- 0.5
gr <- sample_mixed_graph(W, wts, nd, ns, p = 0.1, option = 2)
out <- separate_dense_and_sparse(gr)
out

Adds stars to nodes

Description

Adds stars to nodes

Usage

star_f1(xvals, t)

Arguments

xvals

Values between 0 and 1 from the graphon

t

A parameter indicating the strength of hubs

Value

a vector of values

Examples

# example code
st <- star_f1(runif(10), 3)
st

Adds stars to nodes

Description

Adds stars to nodes

Usage

star_f2(xvals, t)

Arguments

xvals

Values between 0 and 1 from the graphon

t

A parameter indicating the strength of hubs

Value

a vector of values

Examples

# example code
st <- star_f2(runif(10), 3)
st

Adds stars to nodes

Description

Adds stars to nodes

Usage

star_f3(xvals, t)

Arguments

xvals

Values between 0 and 1 from the graphon

t

A parameter indicating the strength of hubs

Value

a vector of values

Examples

# example code
st <- star_f3(runif(10), 3)
st

Adds stars to nodes

Description

Adds stars to nodes

Usage

star_f4(xvals, t)

Arguments

xvals

Values between 0 and 1 from the graphon

t

A parameter indicating the strength of hubs

Value

a vector of values

Examples

# example code
st <- star_f4(runif(10), 3)
st

Adds stars to nodes

Description

Adds stars to nodes

Usage

star_f5(xvals, t)

Arguments

xvals

Values between 0 and 1 from the graphon

t

A parameter indicating the strength of hubs

Value

a vector of values

Examples

# example code
st <- star_f5(runif(10), 3)
st