Some references that need exploring

George S. Fishman. 1986. A Comparison of Four Monte Carlo Methods for Estimating the Probability of s-t Connectedness. IEEE Trans. Reliability 35, 2 (1986).

Ruoming Jin, Lin Liu, Bolin Ding, and Haixun Wang. 2011. Distance-Constraint Reachability Computation in Uncertain Graphs. PVLDB 4, 9 (2011).

Michalis Potamias, Francesco Bonchi, Aristides Gionis, and George Kollios. 2010. k-Nearest Neighbors in Uncertain Graphs. PVLDB 3, 1 (2010).

Zhaonian Zou, Hong Gao, and Jianzhong Li. 2010. Discovering frequent subgraphs over uncertain graph databases under probabilistic semantics. In KDD.