assort: Assortativity Coefficient

In mbojan/isnar: Introduction to Social Network Analysis with R

Description

Assortativity coefficient is a measure of segregation for social networks due to Mark Newman (2002).

Usage

assort(object, ...)

## S3 method for class 'table'
assort(object, ...)

## S3 method for class 'igraph'
assort(object, vattr, ...)

## Default S3 method:
assort(object, ...)

Arguments

object	R object, see available methods
...	other arguments to/from other methods
vattr	character, name of the vertex attribute for which the measure is to be calculated

Details

The measure evaluates the relative prevalence of within-group ties. It is based on the contact layer of the mixing matrix.

Assortativity coefficient is 1 if all ties are within-group. The minimum can be negative, but not less than -1, and depends on the relative number of ties of nodes in different groups. If the network conforms to "proportionate mixing", the coefficient is 0.

If object is a table it is treated as a mixing matrix. Two-dimensional table is interpreted as a contact layer. Three-dimensional table is interpreted as a full mixing matrix m[ghy] cross-classyfying all dyads, in which 'g' and 'h' correspond to group membership of ego and alter respectively. Layers y=1 and y=2 are assumed to be non-contact and contact layers respectively. In the 3-d case only g[,,2] is used.

If g is an object of class "igraph" the measure is calculated for the vertex attribute specified with vattr.

For any other classes, object g are coerced to a table and the table method is called.

Value

Numeric value of the index.

References

Newman, M. J. and Girvan, M. (2002) "Mixing patterns and community structure in networks", arXiv:cond-mat/0210146v1

Newman, M. J. (2003) "Mixing patterns in networks" arXiv:cond-mat/0209450v2

See Also

Mixing matrices: mixingm

Other segregation measures: coleman, ei, freeman, gamix, orwg, smi, ssi

Examples

assort(Wnet, "gender")
assort(EFnet, "type")


if( require(igraph, quietly = TRUE) ) {
  # value of 'assort' for full networks of different sizes
  f <- function(n)
  {
    gfull <- graph.full(n, directed=FALSE)
    V(gfull)$type <- rep(1:2, length=vcount(gfull))
    assort(gfull, "type")
  }
  set.seed(1)
  x <- sort(sample(5:100, 25) * 2)
  y <- sapply(x, f)
  plot(x, y, type="o",
       xlab="Network size", ylab="Assortativity coefficient",
       main="Assortativity coef. for full networks of different sizes")
}

mbojan/isnar documentation built on Feb. 18, 2021, 4:38 a.m.