This study introduces a novel reservoir computing framework featuring an evolvable topology, optimized for minimal clustering degree and path length, which are key characteristics identified as beneficial for reservoir performance. We implement this framework in memristive circuits, enabling dynamic on-chip adaptation and evolution of the topology. We evaluate the efficacy of our memristive reservoir in a wave generation task and two time series prediction tasks. Experimental results demonstrate that our approach not only outperforms existing state-of-the-art methods in predictive performance but also reduces the required circuit area compared to other hardware-based reservoir implementations. This enhancement in both efficiency and performance illustrates the potential of our approach for advancing neuromorphic computing applications.