Segregation Matrix Index

Segregation Matrix Index due to Freshtman (1997). A measure of network segregation. Currently (and originally) supports only two groups.

Usage

smi(object, ...)

# S3 method for table
smi(object, normalize = TRUE, ...)

# S3 method for igraph
smi(object, vattr, ...)

# S3 method for default
smi(object, ...)

Arguments

object

R object, see Details for available methods

...

other arguments passed to/from other methods

normalize

logical, whether normalized values should be returned, defaults to TRUE

vattr

character, name of the node attribute designating groups

Value

Numeric vector of length equal to the number of groups in g

according to vattr with the values of SMI for the groups.

Details

The Segregation Matrix Index (SMI) is calculated for every group separately. It compares the density within group to the density of between group ties of nodes belonging to that group.

Non-normalized version is the ratio of the within-group density to the between-group density, so vary between 0 and infinity. The normalized version varies between 0 and 1.

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.

References

Freshtman, M. (1997) "Cohesive Group Segregation Detection in a Social Network by the Segregation Matrix Index", Social Networks, 19:193--207

See also

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

Examples

# smi() needs a directed network
smi( igraph::as.directed(WhiteKinship, "mutual"), "gender")
#>    female      male 
#> 0.2500000 0.3207547