nd.graphon {NetworkDistance}

Graphon Estimates Distance

Description

Graphon is a symmetric measurable function

W:[0,1]^2\rightarrow[0,1]

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.

Usage

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.

Value

a named list containing

D

an (N\times N) matrix or dist object containing pairwise distance measures.

References

Mukherjee SS, Sarkar P, Lin L (2017). “On clustering network-valued data.” In Guyon I, Luxburg UV, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R (eds.), Advances in neural information processing systems 30, 7071–7081. Curran Associates, Inc.

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)