Compatible dual graphs generated by our enumeration algorithm by connecting the new vertex (blue segment) to the starting graph 3 1 (red). Of the 31 graphs generated using the edge combinations listed in Figure 3, 25 graphs shown here follow all dual graph rules (see Supplementary Figure S1 for the remaining 6 graphs that do not follow our RNA dual graph rules). The 15 non-isomorphic graphs selected to be part of the dual graph library are shown in black boxes. The other 10 graphs, 2, 7, 8, 12, 14, 15, 21, 23, 24, and 25, are isomorphic to graphs 1, 4, 3, 10, 11, 9, 17, 20, 18, and 16, respectively.