Title: An effective method for profiling core-periphery structures in complex networks Show Chinese title

Title: 一种在复杂网络中分析核心-边缘结构的有效方法

Abstract: 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. Show Chinese abstract

Abstract: 对网络中的核心-边缘结构进行分析已引起广泛关注，这导致了各种方法的开发。 其中，富核心方法因其完全无参数且可扩展到大型网络而脱颖而出。 然而，它识别的核心并不总是具有结构性的凝聚力，因为它们可能缺乏高链接密度。 在此，我们提出了一种改进的方法，在富核心框架的基础上进行构建。 我们的方法不依赖于节点度数，而是结合了节点的核度$k$以及其在$k$-核内的中心性。 我们将该方法应用于十二个现实世界的网络，并发现所识别的核心通常比从富核心方法中得到的核心更密集。 此外，我们证明了该方法提供了一种自然的方式来识别异常密集的核心，即团，这通常近似或甚至匹配许多现实世界网络中的最大团。 此外，我们将该方法扩展到多层网络，并展示了其在几个广泛研究的数据集上识别密集多层核心的有效性。 我们的研究可能为探索复杂网络的中尺度特性提供有价值的见解。