There is no tool for that in yEd.
In a complete graph, each node belongs to a directed cycle, because for each set of nodes {v1, ..., vk} the edges {(v1,v2), (v2,v3), ..., (vk,v1)} exist. In other words, this is a trivial problem. However, the number of cycles rises exponentially with the number of nodes. Because the graph is complete, all permutations of a subset form cycles. Moreover, in a graph with n nodes, there are 2^(n-1)-1 subsets with at least two nodes. I.e. there is no efficient way to find/enumerate all cycles. (Which is one reason there is no such tool in yEd.)
