FIGURE 3.

Spanning forests and FPTs. (A) An example graph, G, obtained by taking the graph in Figure 2A and removing the outgoing edge from vertex 5. G has a single terminal SCC containing the single vertex 5. (B) The 24 doubly-rooted spanning forests of G in which 5 is a root (red font) and there is a path from 1 to the other root (also in red font), each with its corresponding product of edge labels. The sum of these 24 edge label products is equal to the numerator of ${\tau }_{\mathrm{1,5}}^{(1)}(G)$ in Eq. 6.