RNA molecules fulfill a large amount of fundamental tasks in every living organism.
To achieve this vast array of functions, from transmitting information to biological sensors, they rely on complex three-dimensional structures.
A low level representation that only considers canonical base pairs, called the secondary structure, has mathematical properties making it suitable for study under a Boltzmann ensemble framework.
Dynamic programming algorithms have shown to be particularly adept to understand the link between secondary structure and sequence in that framework.
Yet this is not enough to fully grasp fine networks of interactions, critical to the function, that are not captured by the secondary structure.

The Leontis-Westhof annotations of non-canonical interactions classifies all interactions beyond those in the secondary structure.
This ontology allows to represent RNA molecules in much more details, and can then be described as directed graph with labelled edges.
The discovery of conserved sub-structures can be transposed to the problem of maximal edge sub-isomorphismes.
While classically NP-hard, we can take advantage of structural properties to restrain the ensemble of admissible graphs.
In this talk, I will present the algorithms we developed for that case and interesting results that where obtained [1].
I will show utilities we offer to the community to analyze known and new structures, through our website carnaval.lri.fr.
In particular, I will highlight the hierarchical organization of sub-structures, and how they are spread over vastly different functions.

I will then speculate briefly over the role of chemical-modifications and future work.

[1] Mining for recurrent long-range interactions in RNA structures reveals embedded hierarchies in network families; Reinharz, Soule, Westhof, Waldispuhl and Denise; NAR, 2018