Cognitive Radio Technology has brought new insights to the problems of spectrum scarcity and inefficiency, in which spectrum holes are opportunistically accessed when the licensed users (primary users) are not using the frequencies that are assigned to those users. In this paper, we propose a multi path route discovery algorithm for cognitive radio ad hoc networks (CRAHN) using algebraic connectivity. The employed routing mechanism takes into account the impact of the primary users on the non-licensed users (secondary users) in a way that the secondary users choose the paths which are less affected by the non-licensed users. With regard to proposed route discovery algorithm, data traffic congestions are tried to be avoided in the secondary network by reducing the number of all possible paths from source to destination. The results show that the devised method overcomes the technique of the route request (RREQ) message flooding between a source and a destination.