# assort: Assortativity Coefficient In netseg: Measures of Network Segregation and Homophily

 assort R Documentation

## Assortativity Coefficient

### Description

Assortativity coefficient is a measure of segregation for social networks due to Newman & Girvan (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 interpreted 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.

If `object` is of class "igraph" it is required to supply `vattr` with the name of the vertex attribute to calculate intermediate mixing matrix.

For any other classes, `object` is 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

Mixing matrices: `mixingm()`

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

### Examples

``````assort(WhiteKinship, "gender")
assort(EF3, "type")

# Values of `assort()` for full networks of different sizes
if( requireNamespace("igraph", quietly = TRUE) ) {
f <- function(n) {
gfull <- igraph::make_full_graph(n, directed=FALSE)
igraph::V(gfull)\$type <- rep(1:2, length = igraph::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")
}
``````

netseg documentation built on July 9, 2023, 6:33 p.m.