Discovering clusters remains challenging when dealing with complex data structures, including those with varying densities, arbitrary shapes, weak separability, or the presence of noise. In this article, we propose a novel clustering algorithm called representative point-based clustering with neighborhood information (RPC-NI), which highlights the significance of neighborhood information often overlooked by existing clustering methods. The proposed algorithm first introduces a new local centrality metric that integrates both neighborhood density and topological convergence to identify core representative points, effectively capturing the structural characteristics of the data. Subsequently, a density-adaptive distance is defined to evaluate dissimilarities between these core representative points, and such distance is used to construct a minimum spanning tree (MST) over these points. Finally, an MST-based clustering algorithm is employed to yield the desired clusters. Incorporating neighborhood information enables RPC-NI to comprehensively determine representative points, and having multiple representative points per cluster allows RPC-NI to adapt to clusters of arbitrary shapes, varying densities, and different sizes. Extensive experiments on widely used datasets demonstrate that RPC-NI outperforms baseline algorithms in terms of clustering accuracy and robustness. These results provide further evidence for the importance of incorporating neighborhood information discovering clusters with complex structures.