Statistical Significance Testing
Note that the Overviews refer to clustering algorithms and do not mention anything about statistical significance testing. In fact, Cluster Analysis is not as much a typical statistical test as it is a "collection" of different algorithms that "put objects into clusters."
The point here is that, unlike many other statistical procedures, cluster analysis methods are mostly used when we do not have any a priori hypotheses, but are still in the exploratory phase of our research. In a sense, cluster analysis finds the "most significant solution possible." Therefore, statistical significance testing in the traditional sense of this term is really not appropriate here, even in cases when p-levels are reported (as in k-means clustering).