I have tried this both on the latest 0.16.1 version and on the latest bleeding edge version of sklearn '0.17.dev0' and this appears to be an issue in both.

I use sklearn.cluster.AgglomerativeClustering(affinity='precomputed',connectivity=Cmat,linkage='complete')
where Cmat is a connectivity matrix in which there are disconnected components.
As indicated by the source code, I get the error message UserWarning: the number of connected components of the connectivity matrix is *>1. Completing it to avoid stopping the tree early.

However, reading the source code I see that when completing the connectivity matrix the developers are wondering whether the clustering can take place without completing the matrix:
""XXX: Can we do without completing the matrix?""

I am interested exactly in this development. Do you think sklearn is planning to fix this and make it possible to do the clustering without completing the matrix? I think it should not be too hard.

Best,
Zhana