freeman: Generalized Freeman's segregation index

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

Description

Calculate Freeman's segregation index for undirected netoworks with arbitrary number of groups.

Usage

freeman(object, ...)

## S3 method for class 'table'
freeman(object, gsizes = NULL, more = FALSE,
  loops = FALSE, ...)

## S3 method for class 'igraph'
freeman(object, vattr, gsizes = NULL,
  loops = any(is.loop(object)), ...)

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

Arguments

object	R object, see Details for available methods
...	other arguments passed to/from other methods
gsizes	numeric, optional true distribution of types, see Details
more	logical, should some more output be returned
loops	logical, whether loops are allowed
vattr	character scalar or any vector of length equal to vcount(object), name of the vertex attribute in object designating the groups or a vector with the attribute itself

Details

Freeman's segregation index (Freeman, 1978) is designed to capture the extent to which the defined groups of vertices tend to have more edges with vertices from the same group than with other groups. Formally, the index compares the observed number of between-group ties with the number of between-group ties that would be expected if ties would be created randomly.

The index has some discontinuity as there are network and group configurations that are characterized by the higher number of between-group ties that is expected under a random graph. The index is truncates these situations and takes a value of 0.

The original Freeman's formulation was for only two types of vertices. Here it is extended to the arbitrary number of types. The modification only affects the way in which the expected number of inter-type edges under pure random graph is calculated.

The function internally calculates the frequency of types of vertices in the supplied attributer vattr. However, it is possible to override this by specifying “true” type distribution with the dis argument. It is assumed to be a table (as returned by table) or a numeric vector with frequencies of types of vertices. This may be especially usefull when dealing with large graphs with larger number of isolates.

Method for mixing matrices

Method for "igraph"s

Value

The value of the Freeman's index.

If more is TRUE, some intermediate results are returned in a list.

References

Freeman, Linton C. (1978) Segregation in Social Networks, Sociological Methods & Research 6(4):411–429

See Also

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

Examples

## White's data from Freeman's article
# segregation level
freeman(Wnet, "gender")
# using 'more' argument
freeman(Wnet, "gender", more=TRUE)

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