diagonals in a network
A typical example in which diagonals
can be helpful is Social Network
Analysis. For example, if we use matrices to represent friendship
perceptions between individuals, then we need a dyadic matrix.
# generate a dyadic matrix for 3 individuals
m <- matrix(sample(0:1, 9, replace=TRUE), nrow=3, ncol=3)
m
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 0
## [3,] 0 1 0
Let says that we want to look at second-order connections (i.e. friends
of friends). If we now want to represent the data from both time period
in a single object, we need a 4-dimensional array. Higher-order arrays
are hard to visualise, another way of doing this is by representing two
dimensions along each of the two edges of a matrix. We can do this using
the Knonecker Product (denoted ⊗), which we can call in R
using
the alias %x%
.
M <- m %x% m
M
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,] 1 1 1 1 1 1 1 1 1
## [2,] 1 1 0 1 1 0 1 1 0
## [3,] 0 1 0 0 1 0 0 1 0
## [4,] 1 1 1 1 1 1 0 0 0
## [5,] 1 1 0 1 1 0 0 0 0
## [6,] 0 1 0 0 1 0 0 0 0
## [7,] 0 0 0 1 1 1 0 0 0
## [8,] 0 0 0 1 1 0 0 0 0
## [9,] 0 0 0 0 1 0 0 0 0
Feelings of friendship towards oneself aren’t always particularly
insightful. We can now use the diagonals
library to eliminate those.
# load the library
library(diagonals)
##
## D I
## A G
## O N
## A L
## S
# remove the elements along the diagonal of width 2
minus_block_matrix(M, size=3)
## Error in eval(expr, envir, enclos): could not find function "minus_block_matrix"
The diagonals package now available on CRAN and can therefore be install directly from inside R
using:
install.packages("diagonals")
Subsequently the package can be loaded using:
library(diagonals)
The above demonstration is also available as a vignette that is included in the package.
It can be accessed from R
using:
vignette("network")
A general introduction to diagonals
is available in next weeks post: diagonals. This post is also available as a vignette that is included in the package
For more information on the package and its development please see yesterday’s post diagonals on CRAN.