  We consider communities whose vertices are predominantly connected, i.e., the
vertices in each community are stronger connected to other community members of
the same community than to vertices outside the community. Flake et al.
introduced a hierarchical clustering algorithm that finds such predominantly
connected communities of different coarseness depending on an input parameter.
We present a simple and efficient method for constructing a clustering
hierarchy according to Flake et al. that supersedes the necessity of choosing
feasible parameter values and guarantees the completeness of the resulting
hierarchy, i.e., the hierarchy contains all clusterings that can be constructed
by the original algorithm for any parameter value. However, predominantly
connected communities are not organized in a single hierarchy. Thus, we develop
a framework that, after precomputing at most $2(n-1)$ maximum flows, admits a
linear time construction of a clustering $\C(S)$ of predominantly connected
communities that contains a given community $S$ and is maximum in the sense
that any further clustering of predominantly connected communities that also
contains $S$ is hierarchically nested in $\C(S)$. We further generalize this
construction yielding a clustering with similar properties for $k$ given
communities in $O(kn)$ time. This admits the analysis of a network's structure
with respect to various communities in different hierarchies.
