  For Leavitt path algebras, we show that whereas removing sources from a graph
produces a Morita equivalence, removing sinks gives rise to a recollement
situation. In general, we show that for a graph $E$ and a finite hereditary
subset $H$ of $E^0$ there is a recollement $$\xymatrix{ L_K(E/\overline H)
\rModd \ar[r] & \ar@<3pt>[l] \ar@<-3pt>[l] L_K(E) \rModd \ar[r] & \ar@<3pt>[l]
\ar@<-3pt>[l] L_K(E_H) \rModd .}$$ We record several corollaries.
