Yes, indeed, I should have posted the exact reference.
I meant this algorithm, yes: Donald B. Johnson: Finding All the Elementary Circuits of a Directed Graph. SIAM Journal on Computing. Volumne 4, Nr. 1 (1975), pp. 77-84.
Another link to the article (for free, and legally): https://www.cs.tufts.edu/comp/150GA/homeworks/hw1/Johnson%2075.PDF
It relies on Tarjan’s algorithm to find the strongly connected components (as the elementary circuits are found within each of the strongly connected components):
Robert Tarjan: Depth-first search and linear graph algorithms. In: SIAM Journal on Computing. Volume 1, Nr. 2 (1972), pp. 146-160.
A link to the article (for free, and legally): https://www.semanticscholar.org/paper/Depth-First-Search-and-Linear-Graph-Algorithms-Tarjan/385742fffcf113656f0d3cf6c06ef95cb8439dc6
For my particular use I didn’t encounter performance/memory issues related to the number of elementary circuits (I typically have 1000+ vertices and 1000+ edges). So it was possible to output the complete list.
I agree there should be some restrictions for bigger graphs: on the length of the circuits perhaps?
[EDIT]: OK, that’s what is already done in igraph_cliques_callback.