Symmetrize an adjacency matrix
to_symmetric_matrix(
g,
rule = c("weak", "mutual", "out", "in", "average", "max", "min"),
na.rm = TRUE
)input matrix
character, which rule to follow when deciding how to symmetrize
logical, should missing values for the cells be ignored? This is
used for the rules "average", "max", or "min". For rules "out" and "in", the
NA is copied over if it is in a cell that is copied by the rule.
Under "weak", a NA is copied if it is in either i->j or j->i and the
other edges is not 1. Under "mutual", a NA is copied if it is in
either i->j or j->i and the other edges is 1.
symmatrized matrix
Turn a (adjacency) matrix into a symmetric one, according to several potential rules.
The diagonal of the matrix remains unaffected.
Rule out: g is made symmetric by copying the upper triangle
onto the lower triangle.
Rule in: g is made symmetric by copying the lower triangle
onto the upper triangle.
Rule weak: every edge is assumed to be reciprocated. Hence, an edge
from $i$ to $j$ also becomes an edge from $j$ to $i$,
Mathematically: i<->j iff i->j or i<-j (OR rule)
Rule mutual: every edge is only maintained if it is already reciprocated
in g. Hence, if an edge from $i$ to $j$ exist and also from $j$ to $i$,
these edges are maintained in the resulting matrix. Otherwise (for unreciprocated
edges or null dyads), the resulting matrix will neither contain an edge
from $i$ to $j$ nor from $j$ to $i$.
Mathematically: i<->j iff i->j and i<-j (AND rule)
Rule average: the values for the edges ($i$, $j$) and ($j$, $i$) are
averaged and assigned to both edges in the resulting matrix. This will
typically result in a non-binary matrix.
Rule max: edges ($i$, $j$) and ($j$, $i$) are both assigned the highest value
of the two edges. If input matrix g is binary, this will yield the
same result as rule weak.
Rule min: edges ($i$, $j$) and ($j$, $i$) are both assigned the lowest value
of the two edges. If input matrix g is binary, this will yield the
same result as rule mutual.
m <- matrix(c(0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,1,0,1,0,1,1,0,0,1,0), byrow = TRUE, ncol = 5)#'
m
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 1 1 0 1
#> [2,] 0 0 1 0 0
#> [3,] 0 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 0 1 0
to_symmetric_matrix(m, "out")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 1 1 0 1
#> [2,] 1 0 1 0 0
#> [3,] 1 1 0 1 1
#> [4,] 0 0 1 0 1
#> [5,] 1 0 1 1 0
to_symmetric_matrix(m, "in")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 0 1 1
#> [2,] 0 0 1 0 0
#> [3,] 0 1 0 1 0
#> [4,] 1 0 1 0 1
#> [5,] 1 0 0 1 0
to_symmetric_matrix(m, "weak")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 1 1 1 1
#> [2,] 1 0 1 0 0
#> [3,] 1 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 1 1 0
to_symmetric_matrix(m, "mutual")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 0 0 1
#> [2,] 0 0 1 0 0
#> [3,] 0 1 0 1 0
#> [4,] 0 0 1 0 1
#> [5,] 1 0 0 1 0
to_symmetric_matrix(m, "average")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0 0.5 0.5 0.5 1.0
#> [2,] 0.5 0.0 1.0 0.0 0.0
#> [3,] 0.5 1.0 0.0 1.0 0.5
#> [4,] 0.5 0.0 1.0 0.0 1.0
#> [5,] 1.0 0.0 0.5 1.0 0.0
to_symmetric_matrix(m, "max")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 1 1 1 1
#> [2,] 1 0 1 0 0
#> [3,] 1 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 1 1 0
to_symmetric_matrix(m, "min")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 1 1 0 1
#> [2,] 0 0 1 0 0
#> [3,] 0 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 0 1 0
m[1, 2] <- m[3, 1] <- NA
m
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 NA 1 0 1
#> [2,] 0 0 1 0 0
#> [3,] NA 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 0 1 0
to_symmetric_matrix(m, "out")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 NA 1 0 1
#> [2,] NA 0 1 0 0
#> [3,] 1 1 0 1 1
#> [4,] 0 0 1 0 1
#> [5,] 1 0 1 1 0
to_symmetric_matrix(m, "in")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 NA 1 1
#> [2,] 0 0 1 0 0
#> [3,] NA 1 0 1 0
#> [4,] 1 0 1 0 1
#> [5,] 1 0 0 1 0
to_symmetric_matrix(m, "weak")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 NA 1 1 1
#> [2,] NA 0 1 0 0
#> [3,] 1 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 1 1 0
to_symmetric_matrix(m, "mutual")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 NA 0 1
#> [2,] 0 0 1 0 0
#> [3,] NA 1 0 1 0
#> [4,] 0 0 1 0 1
#> [5,] 1 0 0 1 0
to_symmetric_matrix(m, "average")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0 0 1.0 0.5 1.0
#> [2,] 0.0 0 1.0 0.0 0.0
#> [3,] 1.0 1 0.0 1.0 0.5
#> [4,] 0.5 0 1.0 0.0 1.0
#> [5,] 1.0 0 0.5 1.0 0.0
to_symmetric_matrix(m, "max")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 0 1 1 1
#> [2,] 0 0 1 0 0
#> [3,] 1 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 1 1 0
to_symmetric_matrix(m, "min")
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0 NA 1 0 1
#> [2,] 0 0 1 0 0
#> [3,] NA 1 0 1 1
#> [4,] 1 0 1 0 1
#> [5,] 1 0 0 1 0