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In this paper, we analyze the outage probability of the multiple-relay cooperative networks with opportunistic relaying and incremental relaying (OIR) over independent but not identically distributed Nakagami-m fading channels. When the fading severity parameters (i.e., m) are integer, a lower bound on the outage probability is obtained, which is shown to be tight at high signal to noise ratio (SNR) regime. An approximate expression is also derived at asymptotic high SNR regime to analyze the diversity order of the system. The diversity order of OIR is found to be the summation of all minimum values of the two fading severity parameters corresponding to each source-relay-destination link plus the fading severity parameter of the direct link (i.e., the source-destination link). The approximate expression is further shown to be tighter than the lower bound, relative to the simulated results, at medium SNR regime and coincides with it at high SNR regime. Simulation results are finally presented to validate the analysis.