  The cluster analysis of very large objects is an important problem, which
spans several theoretical as well as applied branches of mathematics and
computer science. Here we suggest a novel approach: under assumption of local
convergence of a sequence of finite structures we derive an asymptotic
clustering. This is achieved by a blend of analytic and geometric techniques,
and particularly by a new interpretation of the authors' representation theorem
for limits of local convergent sequences, which serves as a guidance for the
whole process. Our study may be seen as an effort to describe connectivity
structure at the limit (without having a defined explicit limit structure) and
to pull this connectivity structure back to the finite structures in the
sequence in a continuous way.
