Advances in graph algorithmics have allowed in-depth study of many natural objects from molecular biology or chemistry to social networks. Particularly in molecular biology and cheminformatics, understanding complex structures by identifying conserved sub-structures is a key milestone towards the artificial design of novel components with specific functions. Given a dataset of structures, we are interested in identifying all maximum common connected partial subgraphs between each pair of graphs, a task notoriously NP-Hard. In this work, we present parallel algorithms over shared and distributed memory to enumerate all maximal connected common sub-graphs between pairs of arbitrary multi-directed graphs with labels on their edges. We offer an implementation of these methods and evaluate their performance on the non-redundant dataset of all known RNA 3D structures. We show that we can compute the exact results in a reasonable time for each pairwise comparison while taking into account a much more diverse set of interactions—resulting in much denser graphs—resulting in an order of magnitude more conserved modules. All code is available at https://gitlab.info.uqam.ca/cbe/pasigraph and results in the branch results.