  We study the topological structure of $SU(3)$ lattice gluodynamics by cluster
analysis. This methodological study is meant as preparation for full QCD. The
topological charge density is becoming visible in the process of overimproved
gradient flow, which is monitored by means of the the Inverse Participation
Ratio (IPR). The flow is stopped at the moment when calorons dissociate into
dyons due to the overimproved character of the underlying action. This gives
the possibility to simultaneously detect all three dyonic constituents of KvBLL
calorons in the gluonic field. The behaviour of the average Polyakov loop under
(overimproved) gradient flow could be also (as its value) a diagnostics for the
actual phase the configuration is belonging to. Timelike Abelian monopole
currents and specific patterns of the local Polyakov loop are correlated with
the topological clusters.The spectrum of reconstructed cluster charges $Q_{cl}$
corresponds to the phases. It is scattered around $Q_{cl} \approx \pm 1/3$ in
the confined phase, whereas it is $Q_{cl} \approx \pm 0.5 \div 0.7$ for heavy
dyons and $|Q_{cl}| < 0.3$ for light dyons in the deconfined phase. Heavy dyons
are increasingly suppressed with increasing temperature. The paper is dedicated
to the memory of Michael Mueller-Preussker who was a member of our research
group for more than twenty years.
