Cohesion Threshold for Strong Ties

Given a cohesion matrix, provides the value of the threshold above which values of cohesion are considered "particularly strong".

Usage

strong_threshold(c)

Arguments

c

A cohesion_matrix object, a matrix of cohesion values (see cohesion_matrix).

Value

The value of the threshold.

Details

The threshold considered in Berenhaut, Moore, and Melvin (2022) which may be used for distinguishing between strong and weak ties. The threshold is equal to half the average of the diagonal of the cohesion matrix, see Berenhaut, Moore, and Melvin (2022).

References

K. S. Berenhaut, K. E. Moore, R. L. Melvin, A social perspective on perceived distances reveals deep community structure. Proc. Natl. Acad. Sci., 119(4), 2022.

Examples

C <- cohesion_matrix(dist(exdata1))
strong_threshold(C)
#> [1] 0.08866922
mean(diag(C)) / 2
#> [1] 0.08866922

## points whose cohesion are greater than the threshold may be considered
## (strong) neighbors
which(C[3, ] > strong_threshold(C))
#> 1 3 4 
#> 1 3 4 

## note that the number of (strongly-cohesive) neighbors varies across the
## space
which(C[4, ] > strong_threshold(C))
#> 2 3 4 6 
#> 2 3 4 6 
C[4, c(2, 3, 4, 6)] # cohesion values can provide neighbor weights
#>          2          3          4          6 
#> 0.10425170 0.10425170 0.17874150 0.09540816