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.

{% highlight r %}

generate a dyadic matrix for 3 individuals

m <- matrix(sample(0:1, 9, replace=TRUE), nrow=3, ncol=3) m {% endhighlight %}

{% highlight text %}

[,1] [,2] [,3]

[1,] 1 1 1

[2,] 1 1 0

[3,] 0 1 0

{% endhighlight %}

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%.

{% highlight r %} M <- m %x% m M {% endhighlight %}

{% highlight text %}

[,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

{% endhighlight %}

Feelings of friendship towards oneself aren’t always particularly insightful. We can now use the diagonals library to eliminate those.

{% highlight r %}

load the library

library(diagonals) {% endhighlight %}

{% highlight text %}

D I

A G

O N

A L

S

{% endhighlight %}

{% highlight r %}

remove the elements along the diagonal of width 2

minus_block_matrix(M, size=3) {% endhighlight %}

{% highlight text %}

Error in eval(expr, envir, enclos): could not find function “minus_block_matrix”

{% endhighlight %}

The diagonals package now available on CRAN and can therefore be install directly from inside R using:

{% highlight r %} install.packages(“diagonals”) {% endhighlight %} Subsequently the package can be loaded using:

{% highlight r %} library(diagonals) {% endhighlight %}

The above demonstration is also available as a vignette that is included in the package. It can be accessed from R using:

{% highlight r %} vignette(“network”) {% endhighlight %}

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.