Node clustering in complex networks based on the euclidean distance of structural characteristics

Node clustering is a technical method for community detection, which combines artificial intelligence clustering algorithms with the structural feature analysis of nodes in complex networks. It is widely used to reveal the underlying structure and functional organization of complex systems with networked structures. In this paper, a novel node clustering method based on the Euclidean distance of nodes’ structural features – specifically, closeness centrality and betweenness centrality – and the k-means++ algorithm is proposed. In this new method, node similarity is quantified by the Euclidean distance between their closeness and betweenness centralities, which incorporate both local and global structural information of the nodes. The clustering process is then performed using the k-means++ algorithm, which improves the initialization of cluster centers and enhances the stability and robustness of clustering results. Experimental results show that this approach effectively distinguishes central and peripheral nodes in networks with core–periphery structures and demonstrates strong adaptability to hierarchical topologies. Further analysis reveals that the clustering of nodes is robust, as the initial network topology has minimal impact on the final structure, while the growth rule plays a decisive role in the distribution of node categories. When the network evolves under the Erdős–Rényi mechanism, node clusters tend to be structurally homogeneous. In contrast, when the network’s growth is governed by the Barabási-Albert process, it leads to the emergence of peripheral-dominated clusters, a pattern that persists as the network size increases. Additionally, the method successfully uncovers the hierarchical structure of networks, as validated in real-world cases. Overall, the clustering method based on the Euclidean distance of structural features provides an innovative and effective tool for revealing structural properties within complex networks.