  We study Markovian stochastic motion on a graph with finite number of nodes
and adiabatically periodically driven transition rates. We show that, under
general conditions, the quantized currents that appear at low temperatures are
a manifestation of topological invariants in the counting statistics of
currents. This observation provides an approach for classification of
topological properties of the counting statistics, as well as for extensions of
the phenomenon of the robust quantization of currents at low temperatures to
the properties of the counting statistics which persist to finite temperatures.
