In the new era of cognitive computing, systems will be able to learn and interact with the environment in ways that will drastically enhance the capabilities of current processors, especially in extracting knowledge from vast amount of data obtained from many sources. Brain-inspired neuromorphic computing systems increasingly attract research interest as an alternative to the classical von Neumann processor architecture, mainly because of the coexistence of memory and processing units. In these systems, the basic components are neurons interconnected by synapses. The neurons, based on their nonlinear dynamics, generate spikes that provide the main communication mechanism. The computational tasks are distributed across the neural network, where synapses implement both the memory and the computational units, by means of learning mechanisms such as spike-timing-dependent plasticity. In this work, we present an all-memristive neuromorphic architecture comprising neurons and synapses realized by using the physical properties and state dynamics of phase-change memristors. The architecture employs a novel concept of interconnecting the neurons in the same layer, resulting in level-tuned neuronal characteristics that preferentially process input information. We demonstrate the proposed architecture in the tasks of unsupervised learning and detection of multiple temporal correlations in parallel input streams. The efficiency of the neuromorphic architecture along with the homogenous neuro-synaptic dynamics implemented with nanoscale phase-change memristors represent a significant step towards the development of ultrahigh-density neuromorphic co-processors.