  In many applications, it is common practice to obtain a network from
interaction counts by thresholding each pairwise count at a prescribed value.
Our analysis calls attention to the dependence of certain methods, notably
Newman--Girvan modularity, on the choice of threshold. Essentially, the
threshold either separates the network into clusters automatically, making the
algorithm's job trivial, or erases all structure in the data, rendering
clustering impossible. By fitting the original interaction counts as given, we
show that minor modifications to classical statistical methods outperform the
prevailing approaches for community detection from interaction datasets. We
also introduce a new hidden Markov model for inferring community structures
that vary over time. We demonstrate each of these features on three real
datasets: the karate club dataset, voting data from the U.S.\ Senate
(2001--2003), and temporal voting data for the U.S. Supreme Court (1990--2004).
