Fig. 1.

A probabilistic network $\mathcal{G}$ (a), its two possible deterministic network topologies G₁ and G₂ (b,c) and a sample bipartite graph between nodes a and d (d) are shown. The bipartite graph ${\mathcal{G}}_{a,d}$ models the dependency between paths connecting nodes a and d in the probabilistic graph shown in (a). H₁, H₂, H₃, H₄ and H₅ are the simple paths between a and d. Collectively these paths yield seven edges, which are {e₁=(a,d),e₂=(b,c), e₃=(b,d),e₄=(a,c),e₅=(c,e),e₆=(b,e),e₇=(e,d)}