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Molecular neuromorphic devices are composed of a random and extremely dense network of single-walled carbon nanotubes (SWNTs) complexed with polyoxometalate (POM). Such devices are expected to have the rudimentary ability of reservoir computing (RC), which utilizes signal response dynamics and a certain degree of network complexity. In this study, we performed RC using multiple signals collected from a SWNT/POM random network. The signals showed a nonlinear response with wide diversity originating from the network complexity. The performance of RC was evaluated for various tasks such as waveform reconstruction, a nonlinear autoregressive model, and memory capacity. The obtained results indicated its high capability as a nonlinear dynamical system, capable of information processing incorporated into edge computing in future technologies.