  The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from
early work published under the name QCM (quasi-clique merger) [Ou2006, Ou2007,
Zhao2011, Qi2014]. The AQCM algorithm performs hierarchical clustering in any
data set for which there is an associated similarity measure quantifying the
similarity of any data i and data j. Importantly, the method exhibits two
valuable performance properties: 1) the ability to automatically return either
a larger or smaller number of clusters depending on the inherent properties of
the data rather than on a parameter 2) the ability to return a very large
number of relatively small clusters automatically when such clusters are
reasonably well defined in a data set. In this work we present the general idea
of a quasi-clique agglomerative approach, provide the full details of the
mathematical steps of the AQCM algorithm, and explain some of the motivation
behind the new methodology. The main achievement of the new methodology is that
the agglomerative process now unfolds adaptively according to the inherent
structure unique to a given data set, and this happens without the time-costly
parameter adjustment that drove the previous QCM algorithm. For this reason we
call the new algorithm \emph{automatic}. We provide a demonstration of the
algorithm's performance at the task of community detection in a social media
network of 22,900 nodes.
