As far as I understand, Hierholzer’s algorithm is one of several methods for constructing Eulerian circuits. I’ve never done so myself, nor checked which algorithm it implements, but one might implement the networkx method for computing these. It appears to be available in the old 1.5 version compatible with IronPython 2.7:
Edit: Here’s a quick implementation @Moria_Schwarz:
230127_EulerianCircuit_NetworkX_00.gh (5.5 KB)