The process of magnetic reconnection in the absence of neutral points is analysed with respect to the topology of the magnetic field. It is shown that the domain of magnetic flux undergoing reconnection comprises regions of different reconnective behaviour. There are regions where the process generates only a certain type of slippage of plasma with respect to the field lines, as well as regions where the magnetic field is reconnected in a way similar to the classical two-dimensional reconnection. It is shown that this behaviour is consistent with the small but non-vanishing production of magnetic helicity in this case. An interpretation of the rate of reconnection for the different regions gives further insights into the complex process of three-dimensional reconnection.