We investigate the outage probability and diversity gain of generalized relay selection (GRS) for network-coded cooperation systems where ${N}$ sources use ${M}$ relays to communicate with a single destination. Although it is common to select a set of the relays with the highest signal-to-noise ratios (SNRs), reasons such as load balancing, scheduling, and others may force the selection of different relays. Thus, it is important to quantify and analyze the performance of any arbitrary selection of ${L}$ relays out of ${M}$ (also known as GRS). We show that the full diversity gain of ${d={M}+1}$ is only persevered when ${L} \ge {N}$ and the set of selected relays includes ${N}$ highest SNR relays.