[R] help about agnes

[Arnau Mir Torres]

Hello.

I have the following distance matrix between 8 points:
     
[1,] 0.000000 3.162278 7.280110 8.544004 7.071068 9.899495 6.403124 8.062258
[2,] 3.162278 0.000000 5.000000 6.403124 4.472136 8.944272 6.082763 8.062258
[3,] 7.280110 5.000000 0.000000 1.414214 1.000000 5.000000 4.242641 5.830952
[4,] 8.544004 6.403124 1.414214 0.000000 2.236068 4.123106 4.472136 5.656854
[5,] 7.071068 4.472136 1.000000 2.236068 0.000000 6.000000 5.000000 6.708204
[6,] 9.899495 8.944272 5.000000 4.123106 6.000000 0.000000 3.605551 3.000000
[7,] 6.403124 6.082763 4.242641 4.472136 5.000000 3.605551 0.000000 2.000000
[8,] 8.062258 8.062258 5.830952 5.656854 6.708204 3.000000 2.000000 0.000000

I want to apply the cluster algorithm using single linkage procedure. 
The metric is the euclidean metric.

In order to do this, I do:

aux=agnes(xMatrix, diss = 
inherits(xMatrix,"dist"),metric="euclidean",method="single")

Next, I do

plot(aux)

because I want to view the dendogram.
My question is about the graph of the dendogram.
What means the number "height" that appears on the left hand of it?
My assumption was it was the distance between clusters but I was wrong 
because
the distance matrices between the clusters are the following:

Join clusters {3} and {5} (distance=1) New matrix distance:

[1,] 0.000000 3.162278 7.071068 8.544004 9.899495 6.403124 8.062258
[2,] 3.162278 0.000000 4.472136 6.403124 8.944272 6.082763 8.062258
[3,] 7.071068 4.472136 0.000000 1.414214 5.000000 4.242641 5.830952
[4,] 8.544004 6.403124 1.414214 0.000000 4.123106 4.472136 5.656854
[5,] 9.899495 8.944272 5.000000 4.123106 0.000000 3.605551 3.000000
[6,] 6.403124 6.082763 4.242641 4.472136 3.605551 0.000000 2.000000
[7,] 8.062258 8.062258 5.830952 5.656854 3.000000 2.000000 0.000000

Join clusters {3,5} and {4} (distance=1.414214). New matrix distance:

[1,] 0.000000 3.162278 7.071068 9.899495 6.403124 8.062258
[2,] 3.162278 0.000000 4.472136 8.944272 6.082763 8.062258
[3,] 7.071068 4.472136 0.000000 4.123106 4.242641 5.656854
[4,] 9.899495 8.944272 4.123106 0.000000 3.605551 3.000000
[5,] 6.403124 6.082763 4.242641 3.605551 0.000000 2.000000
[6,] 8.062258 8.062258 5.656854 3.000000 2.000000 0.000000

Join clusters {7} and {8} (distance = 2). New matrix distance:

[1,] 0.000000 3.162278 7.071068 9.899495 6.403124
[2,] 3.162278 0.000000 4.472136 8.944272 6.082763
[3,] 7.071068 4.472136 0.000000 4.123106 4.242641
[4,] 9.899495 8.944272 4.123106 0.000000 3.000000
[5,] 6.403124 6.082763 4.242641 3.000000 0.000000

etc...
but in the graph of the dendogram, it appears the following numbers when 
it joins the clusters:

cluster {3} and {5}:  more or less 2.3
cluster {3,5} and {4}: more or less 3
cluster {7} and {8}: more or less 4.75.

As you can see, these numbers are distint from the distance between 
clusters (1, 1.414214 and 2).

So, can somebody say me what do these numbers represent?

Thanks in advance,

Arnau.