In contrast to AI hardware, neuromorphic hardware is based on neuroscience, wherein constructing both spiking neurons and their dense and complex networks is essential to obtain intelligent abilities. However, the integration density of present neuromorphic devices is much less than that of human brains. In this report, we present molecular neuromorphic devices, composed of a dynamic and extremely dense network of single-walled carbon nanotubes (SWNTs) complexed with polyoxometalate (POM). We show experimentally that the SWNT/POM network generates spontaneous spikes and noise. We propose electron-cascading models of the network consisting of heterogeneous molecular junctions that yields results in good agreement with the experimental results. Rudimentary learning ability of the network is illustrated by introducing reservoir computing, which utilises spiking dynamics and a certain degree of network complexity. These results indicate the possibility that complex functional networks can be constructed using molecular devices, and contribute to the development of neuromorphic devices.