  The magnetic network observed on the solar surface harbors a sizable fraction
of the total quiet Sun flux. However, its origin and maintenance are not well
known. Here we investigate the contribution of internetwork magnetic fields to
the network flux. Internetwork fields permeate the interior of supergranular
cells and show large emergence rates. We use long-duration sequences of
magnetograms acquired by Hinode and an automatic feature tracking algorithm to
follow the evolution of network and internetwork flux elements. We find that
14% of the quiet Sun flux is in the form of internetwork fields, with little
temporal variations. Internetwork elements interact with network patches and
modify the flux budget of the network, either by adding flux (through merging
processes) or by removing it (through cancellation events). Mergings appear to
be dominant, so the net flux contribution of the internetwork is positive. The
observed rate of flux transfer to the network is 1.5 x 10^24 Mx day^-1 over the
entire solar surface. Thus, the internetwork supplies as much flux as is
present in the network in only 9-13 hours. Taking into account that not all the
transferred flux is incorporated into the network, we find that the
internetwork would be able to replace the entire network flux in approximately
18-24 hours. This renders the internetwork the most important contributor to
the network, challenging the view that ephemeral regions are the main source of
flux in the quiet Sun. About 40% of the total internetwork flux eventually ends
up in the network.
