We study the structure of the magnetic elements in network-cell interiors. A quiet Sun area close to the disc centre was observed with the spectro-polarimeter of the Solar Optical Telescope on board the Hinode space mission, which yielded the best spatial resolution ever achieved in polarimetric data of the Fe I 630 nm line pair. For comparison and interpretation, we synthesize a similar data set from a three-dimensional magneto-hydrodynamic simulation. We find several examples of magnetic elements, either roundish (tube) or elongated (sheet), which show a central area of negative Stokes-V area asymmetry framed or surrounded by a peripheral area with larger positive asymmetry. This pattern was predicted some eight years ago on the basis of numerical simulations. Here, we observationally confirm its existence for the first time. We gather convincing evidence that this pattern of Stokes-V area asymmetry is caused by the funnel-shaped boundary of magnetic elements that separates the flux concentration from the weak-field environment. We also conclude that this kind of magnetic element of the internetwork is accompanied by electric current sheets.