WPGMA
WPGMA (Weighted Pair Group Method with Arithmetic Mean) is a simple agglomerative (bottom-up) hierarchical clustering method, generally attributed to Sokal and Michener.
The WPGMA method is similar to its unweighted variant, the UPGMA method.
Algorithm
The WPGMA algorithm constructs a rooted tree (dendrogram) that reflects the structure present in a pairwise distance matrix (or a similarity matrix). At each step, the nearest two clusters, say 
and 
, are combined into a higher-level cluster 
. Then, its distance to another cluster 
is simply the arithmetic mean of the distances between and members of :
The WPGMA algorithm produces rooted dendrograms and requires a constant-rate assumption: it produces an ultrametric tree in which the distances from the root to every branch tip are equal. This ultrametricity assumption is called the molecular clock when the tips involve DNA, RNA and protein data.
Working example
First step
Let us assume that we have five elements 
and the following matrix 
of pairwise distances between them :
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Become You
by: Indigo GirlsI heard you sing a rebel song,
sung it loud and all alone.
We can't afford the things you save,
we can't afford the warranty.
I see you walking in the glare
down the county road we share.
Our southern blood, my heresy,
damn that ol' confederacy.
It took a long time to
become the thing I am to you.
And you won't tear it apart
without a fight, without a heart.
I'm sorry for what you have learned,
when you feel the tables turn.
To run so hard in your race,
now you find who set the pace.
The landed aristocracy
exploiting all your enmity.
All your daddies fought in vain,
leave you with the mark of Cain.
It took a long time to
become the thing I am to you.
And you won't tear it apart
without a fight, without a heart.
It took a long time to
become you, become you.
The center holds, so they say.
It never held too well for me.
I won't stop short for common ground
that vilifies the trodden down.
The center held the bonded slave
for the sake of industry.
The center held the bloody hand
of the executioner man.
It took a long time to
become the thing I am to you.
And you won't tear it apart
without a fight, without a heart.
It took a long time to