An effective method for profiling core-periphery structures in complex networks

Profiling core-periphery structures in networks has attracted significant attention, leading to the development of various methods. Among these, the rich-core method is distinguished for being entirely parameter-free and scalable to large networks. However, the cores it identifies are not always structurally cohesive, as they may lack high link density. Here, we propose an improved method building upon the rich-core framework. Instead of relying on node degree, our approach incorporates both the node's coreness $k$ and its centrality within the $k$-core. We apply the approach to twelve real-world networks, and find that the cores identified are generally denser compared to those derived from the rich-core method. Additionally, we demonstrate that the proposed method provides a natural way for identifying an exceptionally dense core, i.e., a clique, which often approximates or even matches the maximum clique in many real-world networks. Furthermore, we extend the method to multiplex networks, and show its effectiveness in identifying dense multiplex cores across several well-studied datasets. Our study may offer valuable insights into exploring the meso-scale properties of complex networks.