Circuit-partition unimodality conjecture for weakly Eulerian graphs and digraphs

Let a weakly Eulerian graph or digraph be given, and for each integer $k$ let the number of its partitions into $k$ circuits be counted. Circuit-partition unimodality conjecture. For any weakly Eulerian graph or digraph, the number of partitions into $k$ circuits is unimodal as a function of $k$. The conjecture is motivated by the circuit-counting interpretation of $xq_G(1+x)$ for interlace graphs and would extend the corresponding unimodality assertion beyond the cases directly represented by interlace polynomials.