# Merging more than one cluster in hierarchical clustering

I have this simple example consisting of

• 5 data points X = {A,B,C,D,E}
• the following proximity matrix (higher value = higher similarity)

 | A | B | C | D | E A | - | 9 | 0 | 9 | 3 B | 9 | - | 8 | 4 | 0 C | 0 | 8 | - | 5 | 0 D | 9 | 4 | 5 | - | 7 E | 3 | 0 | 0 | 7 | - 

Given the first row of the matrix, what would happen in the first iteration, if I would apply an agglomerative hierarchical clustering algorithm. Which clusters are merged? Just (A,B) or (A,B,D)? Every example that I could find only merged two clusters per iteration. But in my example Clusters A, B and D have the same proximity/similarity, hence my intuition is to merge all three.