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

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	# 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)

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