Basic Usage of NetworkDistance Package
In NetworkDistance: Distance Measures for Networks

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

1. Load

Surely, the first thing we are always bound to do is to load the package,

library(NetworkDistance)

2. Computing Distances

Suppose you have $N$ network objects represented as square adjacency matrices. All the functions in the package require your data to be in a form of list whose elements are your adjacency matrices. Let's load example data graph20.

data(graph20)     # use `help(graph20)' to see more details.
typeof(graph20)   # needs to be a list

Before proceeding any further, since we have two types of graphs - densely and sparsely connected with $p=0.8$ and $p=0.2$ - we know that the distance matrix should show block-like pattern. Below is two example graphs from the dataset.

suppressMessages(library(igraph))
par(mfrow=c(1,2),pty="s")
plot(graph_from_adjacency_matrix(graph20[[7]], mode="undirected"), vertex.size=7, vertex.label=NA, main="graph No.7", edge.arrow.size=.5)
plot(graph_from_adjacency_matrix(graph20[[18]], mode="undirected"), vertex.size=7, vertex.label=NA, main="graph No.18", edge.arrow.size=.5)

Once you have your data in such a form, all you've got is to run a single-line code to acquire distance numerics, resulting in either a dist class object or a square matrix. For example, let's compute graph diffusion distance by Hammond et al. (2013) on our example set.

dist.gdd <- nd.gdd(graph20)  # return as a 'dist' object

and you can see the discriminating pattern from the distance matrix dist.gdd$D with black represents $0$ and white represents the largest positive number, indicating large deviation from 0.

par(pty="s")
dmat = as.matrix(dist.gdd$D)
image(dmat[,20:1],main="pairwise distance matrix",axes=FALSE,col=gray(0:100/100))

Finally, let's compare different methods as well.

dist.wsd <- nd.wsd(graph20)              # spectrum-weighted distance
dist.dsd <- nd.dsd(graph20, type="SLap") # discrete spectral measure
dist.nfd <- nd.nfd(graph20)              # network flow distance

par(mfrow=c(1,3),pty="s")
image(as.matrix(dist.wsd$D)[,20:1],main="nd.wsd",axes=FALSE,col=gray(0:100/100)) 
image(as.matrix(dist.dsd$D)[,20:1],main="nd.dsd",axes=FALSE,col=gray(0:100/100)) 
image(as.matrix(dist.nfd$D)[,20:1],main="nd.nfd",axes=FALSE,col=gray(0:100/100))

3. One Application : Embedding Networks, Not Network Embedding

Our interest is focused on dealing with a collection of networks, not a single network. Therefore, the example we cover here is to embed multiple networks, not an embedding of single network and its nodes as points. We will use multidimensional scaling to embed 20 graphs we did before.

gdd2 = stats::cmdscale(dist.gdd$D, k=2)  # 2-d embedding from 'gdd' distance
wsd2 = stats::cmdscale(dist.wsd$D, k=2)  #                    'wsd'
dsd2 = stats::cmdscale(dist.dsd$D, k=2)  #                    'dsd'
nfd2 = stats::cmdscale(dist.nfd$D, k=2)  #                    'nfd'

par(mfrow=c(2,2))
plot(gdd2, main="embedding with 'gdd'", pch=19, xlab="x", ylab="y", cex=0.25)
plot(wsd2, main="embedding with 'wsd'", pch=19, xlab="x", ylab="y", cex=0.25)
plot(dsd2, main="embedding with 'dsd'", pch=19, xlab="x", ylab="y", cex=0.25)
plot(nfd2, main="embedding with 'nfd'", pch=19, xlab="x", ylab="y", cex=0.25)

From the figure above, we can see that different measures/metrics reveal a variety of topological or network features. This necessitates the very existence of a package like ours to provide a set of tools for diverse perspectives on the space networks.