Count how many unique eulerian path are in a graph? I know how to check if graph have an eulerian path. But, I wonder, is there any general solution to count, how many unique eulerian path exists in a graph? 

For a case of directed graph there is a polynomial algorithm, bases on BEST theorem about relation between the number of Eulerian circuits and the number of spanning arborescenes, that can be computed as cofactor of Laplacian matrix of graph.
Undirected case is intractable unless $P \ne \#P$.
