The instability of operational channels on cognitive radio networks (CRNs), which is due to the stochastic behavior of primary users (PUs), has increased the complexity of the design of the optimal routing criterion (ORC) in CRNs. The exploitation of available opportunities in CRNs, such as the channel diversity, as well as alternative routes provided by the intermediate nodes belonging to routes (internal backup routes) in the route‐cost (or weight) determination, complicate the ORC design. In this paper, to cover the channel diversity, the CRN is modeled as a multigraph in which the weight of each edge is determined according to the behavior of PU senders and the protection of PU receivers. Then, an ORC for CRNs, which is referred to as the stability probability of communication between the source node and the destination node (SPC_SD), is proposed. SPC_SD, which is based on the obtained model, internal backup routes, and probability theory, calculates the precise probability of communication stability between the source and destination. The performance evaluation is conducted using simulations, and the results show that the end‐to‐end performance improved significantly.