  Using the non-equilibrium Keldysh Green's function formalism, we show that
the non-equilibrium charge transport in nanoscopic quantum networks takes place
via {\it current eigenmodes} that possess characteristic spatial patterns. We
identify the microscopic relation between the current patterns and the
network's electronic structure and topology and demonstrate that these patterns
can be selected via gating or constrictions, providing new venues for
manipulating charge transport at the nanoscale. Finally, decreasing the
dephasing time leads to a smooth evolution of the current patterns from those
of a ballistic quantum network to those of a classical resistor network.
