Extended Data Fig. 1: Streamline geometries in three trivalent network geometries.

To better establish the robustness of our findings we have conducted experiments in three types of periodic trivalent networks. They all correspond to continuous deformations of the honeycomb geometry. (a) Pictures of the three experiments conducted in three different networks. The channel width is the same in the three experiments (200 μm). (b) Close-up on the streamlines corresponding to the region of the network shown in (a). (c) Full geometry of the streamlines. In all three cases they form self-avoiding loops, and the fraction of nodes where the three currents vanish is subdominant but depend on the specific geometry of the nodes. We note that in the brick wall geometry we find some interrupted streamlines due to defects in the design that cause local density fluctuations.