  One of the longstanding problems in spectral graph clustering (SGC) is the
so-called model order selection problem: automated selection of the correct
number of clusters. This is equivalent to the problem of finding the number of
connected components or communities in an undirected graph. In this paper, we
propose AMOS, an automated model order selection algorithm for SGC. Based on a
recent analysis of clustering reliability for SGC under the random
interconnection model, AMOS works by incrementally increasing the number of
clusters, estimating the quality of identified clusters, and providing a series
of clustering reliability tests. Consequently, AMOS outputs clusters of minimal
model order with statistical clustering reliability guarantees. Comparing to
three other automated graph clustering methods on real-world datasets, AMOS
shows superior performance in terms of multiple external and internal
clustering metrics.
