In this paper, we investigate physical layer security of multi-relay non-orthogonal multiple access (NOMA) networks with partial relay selection considering decode-and-forward (DF) and amplify-and-forward (AF) protocols. We propose a partial relay scheme aiming to select the best relay based on the highest signal-to-noise-ratio (SNR) of the first link. We derive new exact and asymptotic expressions for strictly positive secrecy capacity (SPSC) and secrecy outage probability (SOP) considering

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... leigh fading channels. Numerical results demonstrate that AF and DF provide almost a similar secrecy performance. Moreover, they prove that partial relay selection improves SPSC and reduces SOP when the relay-cluster is closer to the legitimate receiver.