Convert asymmetric pairwise matrix to symmetrical pairwise means

This function produces a symmetrical matrix with values representing the pairwise means of directional flows in an asymmetric input matrix. The output can be used in tests about the strength of direction-agnostic connectivity among nodes in a data set (e.g. the "isolation" hypothesis; Kling and Ackerly (2021)).

Usage

pairwise_means(x)

Arguments

x

A square matrix with entries representing directional edge weights between pairs of nodes.

Value

A symmetrical square matrix the same size as x, with values representing the pairwise means of directional flows in x.

References

Kling and Ackerly (2021). Global wind patterns shape genetic differentiation, asymmetric gene flow, and genetic diversity in trees. Proceedings of the National Academy of Sciences 118: e2017317118. doi:10.1073/pnas.2017317118

Examples

# directional flows among three sites, from row to column
x <- matrix(c(0, 2, 6,
              4, 0, 1,
              2, 3, 0), 3, byrow = TRUE)
pairwise_means(x)
#>      [,1] [,2] [,3]
#> [1,]    0    3    4
#> [2,]    3    0    2
#> [3,]    4    2    0