I have cluster consisting of two points and I am working with non-Euclidean distance. I wonder if it is appropriate to talk about center of cluster in this case and how we can interpret it? We can start with simpler case when distance is weighted Euclidean.Update: Here is clarification. Assume we are using Manhattan distance to find centroid of our 2 point cluster. As far as I understand centroid is not unique in this case if we use PAM algorithm. We need to work with whole set of centroids  for one cluster. Hence, clustering might produce random results on each iteration. It looks to me that problem is not well posed. 
Definition - center of the cluster with non-Euclidean distance
clustering;distance