nd_graphon function

Graphon Estimates Distance

Graphon is a symmetric measurable function [REMOVE_ME]$W:[0,1]^2\rightarrow[0,1] [REMOVE_ME_2]$

that is considered to be a generating model for an observed network. nd.graphon computes distances between networks based on the estimated graphons of each network. Estimation methods are taken from graphon package. For more details, see the function links below.

nd.graphon(
  A,
  out.dist = TRUE,
  method = c("completion", "LG", "nbdsmooth", "SBA", "USVT"),
  ...
)

Arguments

• A: a list of length $N$ containing $(M\times M)$ adjacency matrices.
• out.dist: a logical; TRUE for computed distance matrix as a dist object.
• method: type of graphon estimation methods to be used.
• ...: extra parameters to be passed onto graphon estimation functions. See also est.completion, est.LG, est.nbdsmooth, est.SBA, and est.USVT for details.

Returns

a named list containing

• D: an $(N\times N)$ matrix or dist object containing pairwise distance measures.

Description

Graphon is a symmetric measurable function

that is considered to be a generating model for an observed network. nd.graphon computes distances between networks based on the estimated graphons of each network. Estimation methods are taken from graphon package. For more details, see the function links below.

Examples

## load example data
data(graph20)

## compute USVT-based distance
output <- nd.graphon(graph20, out.dist=FALSE, method="usvt")

## visualize
opar = par(no.readonly=TRUE)
par(pty="s")
image(output$D[,20:1], main="USVT", col=gray(0:32/32), axes=FALSE)
par(opar)

References

Rdpack::insert_ref(key="mukherjee_clustering_2017",package="NetworkDistance")