FIGURE 4.

Splitting probabilities. (A) An example graph, G, on six vertices, $\left\{1,\dots ,6\right\}$ , with three SCCs. The partial order is given by {1, 2, 3, 4}⪯{5} and {1, 2, 3, 4}⪯{6}, with {5} and {6} being the two terminal SCCs. (B) The 18 spanning forests of G rooted at vertices 5 and 6 (red font), with those containing a path from 1 to 5 in the green box and those containing a path from 1 to 6 in the purple box. Each spanning forest is shown with its corresponding product of edge labels. The sum of all 18 edge label products is equal to the denominator of π _1,5(G) in Eq. 8; the sum of the six edge label products in the green box is equal to the numerator of π _1,5(G) in Eq. 8.