Calculating the mixing matrix and assortativity coefficient with igraph in R

The mixing matrix of a graph gives the density of edges between vertices with different characteristics. The mixing matrix for a given igraph object can be calculated using the following function:

# calculate the mixing matrix of in igraph graph object ‘mygraph’, by some vertex attribute ‘attrib’

# can change the default use.density=FALSE to return a matrix with raw number of edges rather than density

mixmat <- function(mygraph, attrib, use.density=TRUE) {

require(igraph)

# get unique list of characteristics of the attribute

attlist <- sort(unique(get.vertex.attribute(mygraph,attrib)))

numatts <- length(attlist)

# build an empty mixing matrix by attribute

mm <- matrix(nrow=numatts,

ncol=numatts,

dimnames=list(attlist,attlist))

# calculate edge density for each matrix entry by pairing type

# lends itself to parallel if available

el <- get.edgelist(mygraph,names=FALSE)

for (i in 1:numatts) {

for (j in 1:numatts) {

mm[i,j] <- length(which(apply(el,1,function(x) {

get.vertex.attribute(mygraph, attrib, x[1] ) == attlist[i] &&

get.vertex.attribute(mygraph, attrib, x[2] ) == attlist[j] } )))

}

}

# convert to proportional mixing matrix if desired (ie by edge density)

if (use.density) mm/ecount(mygraph) else mm

}

view rawmixing_matrix.R hosted with ❤ by GitHub

The assortativity coefficient, based on Newman’s paper, can be calculated from the mixing matrix by the following:

# calculate the assortativity coefficient for a mixing matrix of a graph

# ref: MEJ Newman, ‘Mixing patterns in networks’, Phys Rev E 67, 026126 (2003)

#

# define assortativity coefficient as

# trace (m) – sum (m^2)

# ac = ————————-

# 1 – sum (m^2)

# 

# where m is the mixing matrix of a graph

assortcoeff <- function(m) {

tr <- sum(diag(m))

sumsq <- sum (rowSums(m)*colSums(m))

(tr – sumsq) / (1 – sumsq)

}

view rawassortativity_coefficient.R hosted with ❤ by GitHub

Here is an example (be sure to load the functions mentioned above):

# sample calculating mixing matrix and assortativity coefficient with igraph

require(igraph)

set.seed(12)

# create a random graph

g <- random.graph.game(1000,0.15)

# assign some characteristics

V(g)$color <- c(‘red‘,‘white‘,‘blue‘,‘orange‘,‘green‘)

# calculate the mixing matrix

m <- mixmat(g,‘color‘)

# now calculate the assortativity coefficient

assortcoeff(m)

view rawsample_mm_ac.R hosted with ❤ by GitHub

Cool.

Calculating the mixing matrix and assortativity coefficient with igraph in R

Random Posts

Hello world!

Cách Tìm Phương Trình Tiếp Tuyến Của Đồ Thị Hàm Số

Cách Tìm Đường Cao Trong Tam Giác Vuông, Cân, Đều

Cách nhân và chia phân số [Toán tiểu học]

Post Comment Cancel reply

	# calculate the mixing matrix of in igraph graph object ‘mygraph’, by some vertex attribute ‘attrib’
	# can change the default use.density=FALSE to return a matrix with raw number of edges rather than density

	mixmat <- function(mygraph, attrib, use.density=TRUE) {

	require(igraph)

	# get unique list of characteristics of the attribute
	attlist <- sort(unique(get.vertex.attribute(mygraph,attrib)))

	numatts <- length(attlist)

	# build an empty mixing matrix by attribute
	mm <- matrix(nrow=numatts,
	ncol=numatts,
	dimnames=list(attlist,attlist))

	# calculate edge density for each matrix entry by pairing type
	# lends itself to parallel if available
	el <- get.edgelist(mygraph,names=FALSE)
	for (i in 1:numatts) {
	for (j in 1:numatts) {
	mm[i,j] <- length(which(apply(el,1,function(x) {
	get.vertex.attribute(mygraph, attrib, x[1] ) == attlist[i] &&
	get.vertex.attribute(mygraph, attrib, x[2] ) == attlist[j] } )))
	}
	}

	# convert to proportional mixing matrix if desired (ie by edge density)
	if (use.density) mm/ecount(mygraph) else mm
	}

	# calculate the assortativity coefficient for a mixing matrix of a graph
	# ref: MEJ Newman, ‘Mixing patterns in networks’, Phys Rev E 67, 026126 (2003)
	#
	# define assortativity coefficient as
	# trace (m) – sum (m^2)
	# ac = ————————-
	# 1 – sum (m^2)
	#
	# where m is the mixing matrix of a graph

	assortcoeff <- function(m) {
	tr <- sum(diag(m))
	sumsq <- sum (rowSums(m)*colSums(m))
	(tr – sumsq) / (1 – sumsq)
	}

	# sample calculating mixing matrix and assortativity coefficient with igraph

	require(igraph)
	set.seed(12)

	# create a random graph
	g <- random.graph.game(1000,0.15)

	# assign some characteristics
	V(g)$color <- c(‘red‘,‘white‘,‘blue‘,‘orange‘,‘green‘)

	# calculate the mixing matrix
	m <- mixmat(g,‘color‘)

	# now calculate the assortativity coefficient
	assortcoeff(m)

You Might Also Like

Random Posts

Post Comment Cancel reply