The timing verification method for stochastic networks and circuits is a computerized method that includes a Valued-Sum-of-Products (VSOP) tool as an extension to Zero-suppressed Binary Decision Diagrams (ZBDD) to compute and store paths with their corresponding lengths or statistical parameters. This method starts from source vertices and inductively builds a path database in the topological order of gates. At each node the method builds a set of partial paths that terminated that node using VSOP expressions. Path queries are performed on all paths using VSOP operations, thereby querying the top K-most critical paths in integrated circuit networks.