Because the functional repertiore of RNA molecules, like proteins, is closely linked to the diversity of their shapes, uncovering RNA's structural repertoire is vital for identifying novel RNAs, especially in genomic sequences. To help expand the limited number of known RNA families, we use graphical representation and clustering analysis of RNA secondary structures to predict novel RNA topologies and their abundance as a function of size. Representing the essential topological properties of RNA secondary structures as graphs enables enumeration, generation, and prediction of novel RNA motifs. We apply a probabilistic graph-growing method to construct the RNA structure space encompassing the topologies of existing and hypothetical RNAs and cluster all RNA topologies into two groups using topological descriptors and a standard clustering algorithm. Significantly, we find that nearly all existing RNAs fall into one group, which we refer to as "RNA-like"; we consider the other group "non-RNA-like". Our method predicts many candidates for novel RNA secondary topologies, some of which are remarkably similar to existing structures; interestingly, the centroid of the RNA-like group is the tmRNA fold, a pseudoknot having both tRNA-like and mRNA-like functions. Additionally, our approach allows estimation of the relative abundance of pseudoknot and other (e.g. tree) motifs using the "edge-cut" property of RNA graphs. This analysis suggests that pseudoknots dominate the RNA structure universe, representing more than 90% when the sequence length exceeds 120 nt; the predicted trend for <100 nt agrees with data for existing RNAs. Together with our predictions for novel "RNA-like" topologies, our analysis can help direct the design of functional RNAs and identification of novel RNA folds in genomes through an efficient topology-directed search, which grows much more slowly in complexity with RNA size compared to the traditional sequence-based search.