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This paper evaluates the outage probability of cognitive relay networks with cooperation between secondary users based on the underlay approach, while adhering to the interference constraint on the primary user, i.e., the limited amount of interference which the primary user can tolerate. A relay selection criterion, suitable for cognitive relay networks, is provided, and using it, we derive the outage probability. It is shown that the outage probability of cognitive relay networks is higher than that of conventional relay networks due to the interference constraint, and we quantify the increase. In addition, the outage probability is affected by the distance ratio of the interference link (between the secondary transmitter and the primary receiver) to the relaying link (between the secondary transmitter and the secondary receiver). We also prove that cognitive relay networks achieve the same full selection diversity order as conventional relay networks, and that the decrease in outage probability achieved by increasing the selection diversity (the number of relays) is not less than that in conventional relay networks.