  In this paper we propose a graph-based data clustering algorithm which is
based on exact clustering of a minimum spanning tree in terms of a minimum
isoperimetry criteria. We show that our basic clustering algorithm runs in $O(n
\log n)$ and with post-processing in $O(n^2)$ (worst case) time where $n$ is
the size of the data set. We also show that our generalized graph model which
also allows the use of potentials at vertices can be used to extract a more
detailed pack of information as the {\it outlier profile} of the data set. In
this direction we show that our approach can be used to define the concept of
an outlier-set in a precise way and we propose approximation algorithms for
finding such sets. We also provide a comparative performance analysis of our
algorithm with other related ones and we show that the new clustering algorithm
(without the outlier extraction procedure) behaves quite effectively even on
hard benchmarks and handmade examples.
