Fig. 5.

A and B show for two directed six-membered rings, and C shows the distribution of obtained for neat water. When (A), the ring is made up of only DA water molecules, whereas when , the ring consists of one DD, one AA, and four DA water molecules. The blue-colored paths show possible realizations of obtained for these rings. In particular for the ring, the longest outgoing path from the tagged DA water (surrounded by a blue sphere) to waters other than itself, is shown by the blue path that is made of five hydrogen bonds. This path ends at the water surrounded by a yellow sphere. For (B), a realization of the longest outgoing wire for a DD water molecule (surrounded by a blue sphere) is shown by the blue path made up of three hydrogen bonds. This path ends at the water surrounded by the yellow sphere. For clarity, in these figures we only show examples of six-membered rings. However, as discussed in the text, the same features hold for rings of all sizes. The distributions of of charged systems are quite similar (SI Appendix).