freeman  R Documentation 
Calculate Freeman's segregation index for undirected networks with arbitrary number of groups.
freeman(object, ...)
## S3 method for class 'table'
freeman(object, gsizes = NULL, loops = FALSE, ...)
## S3 method for class 'igraph'
freeman(object, vattr, gsizes = NULL, loops = any(is.loop(object)), ...)
## Default S3 method:
freeman(object, ...)
object 
R object, see Details for available methods 
... 
other arguments passed to/from other methods 
gsizes 
numeric, optional true distribution of types, see Details 
loops 
logical, whether loops are allowed 
vattr 
character scalar or any vector of length equal to

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 betweengroup ties with the number of betweengroup ties that would be expected if ties would be created randomly.
Originally the index has a discontinuity for network and group size configurations that are characterized by the higher number of betweengroup ties that is expected under a random graph, for which it returns 0 (as originally described by Freeman (1978)). We removed that truncation such that it returns values betweem 1 and 1.
The original Freeman's formulation involves two groups of vertices. Here it is extended to the arbitrary number of groups. The generalization affects the way in which the expected number of betweengroup edges under pure random graph is calculated, see Bojanowski & Corten (2014) for details.
The function internally calculates the sizes of groups of vertices in the
supplied attribute vattr
. However, it is possible to override this by
specifying "true" type distribution with the gsizes
argument. It is assumed
to be a table (as returned by table()
) or a numeric vector with the group
sizes. This may be especially usefull when dealing with large graphs and/or
with large number of isolates.
If object
is a table it is interpreted as a mixing matrix.
Twodimensional table is interpreted as a contact layer. Threedimensional
table is interpreted as a full mixing matrix m_{ghy}
crossclassyfying 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 noncontact 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.
Method for mixing matrices
Method for "igraph"s
The value of the Freeman's index.
Freeman, Linton C. (1978) Segregation in Social Networks, Sociological Methods & Research 6(4):411–429
Bojanowski, Michał, and Rense Corten. 2014. "Measuring Segregation in Social Networks." Social Networks 39: 14–32. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.socnet.2014.04.001")}
Other segregation measures:
assort()
,
coleman()
,
ei()
,
gamix()
,
orwg()
,
smi()
,
ssi()
## White's data from Freeman's article segregation level
freeman(WhiteKinship, "gender")
# using 'more' argument
freeman(WhiteKinship, "gender")
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