The wealth of the combinatorics of nucleotide base pairs enables RNA molecules to assemble into sophisticated interaction networks, which are used to create complex 3D substructures. These interaction networks are essential to shape the 3D architecture of the molecule, and also to provide the key elements to carry molecular functions such as protein or lig-and binding. They are made of organised sets of long-range tertiary interactions which connect distinct secondary structure elements in 3D structures. Here, we present a de novo data-driven approach to extract automatically from large data sets of full RNA 3D structures the recurrent interaction networks (RINs). Our methodology enables us for the first time to detect the interaction networks connecting distinct components of the RNA structure, highlighting their diversity and conservation through non-related functional RNAs. We use a graphical model to perform pairwise comparisons of all RNA structures available and to extract RINs and modules. Our analysis yields a complete catalog of RNA 3D structures available in the Protein Data Bank and reveals the intricate hierarchical organization of the RNA interaction networks and modules. We assembled our results in an online database (http://carnaval.lri.fr) which will be regularly updated. Within the site, a tool allows users with a novel RNA structure to detect automatically whether the novel structure contains previously observed RINs.