I'm working with 104x42 data set where all variables are (asymmetric) binary (0-1). I've read that Ward's linkage method doesn't work theoretically properly with binary data beaucause it requests Euclidean distance in a space that i presume should be Euclidean. But I also read that it is possible to compute Euclidean distance for binary data. With this distance does it makes sense to cluster with Ward's method? Otherwise, does it make sense with Hamming distance (that is a metric)?
I'd assume that just as with k-means, the use of Bergman divergences is appropriate. Ward is not going to fail badly if you put other measures in it - it's just expecting values from squared deviations.
And on binary vectors, Euclidean, squared Euclidean, and Hamming will be trivially equivalent.
What matters is the kind of clusters found. K-means and Ward correspond to modeling clusters with means, and minimal squared deviations from these means. This is fine if squared deviations from an average make sense for your application. Which may, or may not, be the case. Most likely, there are other, more appropriate choices.