In this paper, an energy harvesting architecture in an Underlay Cooperative Cognitive Network (UCCN) is investigated, in which power constrained Decode-and-Forward relays harvest energy from radio-frequency signals received from a source, and then consume the harvested energy by forwarding the recoded signals to their destination. These recoded signals are launched by a transmitting power which is the harvested energy per a time interval. Based on the energy harvesting architectures that have been studied, two operation protocols are proposed: UCCN with Power Splitting architecture (UCCN-PS), and UCCN with Time Switching architecture (UCCN-TS). The best cooperative relay in both protocols is taken to be the one that satisfies the following conditions: maximum harvested energy, and maximum decoding capacity. As a result of the best relay selection, the signal quality of the selected link from the best relay to the destination is enhanced by the maximum harvested energy. The system performance of the secondary network in the UCCN-PS and UCCN-TS protocols is analyzed and evaluated by the exact closed-form outage probabilities and throughput analyses over Rayleigh fading channels. The Monte Carlo simulation method is performed to verify the theoretical expressions. Evaluations based on outage probability and throughput show that the system performance of the secondary network in the UCCN-PS and UCCN-TS protocols improves when the number of cooperative relays and the interference constraint increase as well as when the primary receiver is farther from the transmitting nodes such as the source and relays of the secondary network. In addition, the throughput performance of the UCCN-PS protocol outperforms that of the UCCN-TS protocol. Finally, the effects of the power splitting ratio, energy harvesting time, energy conversion efficiency, target Signal-to-Noise Ratio (SNR), and location of cooperative relays on the system performance of the secondary network are presented and discussed.