Core–periphery structure is an emerging property of a wide range of complex systems and indicate the presence of group of actors in the system with an higher number of connections among them and a lower number of connections with a sparsely connected periphery. The dynamics of a complex system which is interacting on a given graph structure is strictly connected with the spectral properties of the graph itself, nevertheless it is generally extremely hard to obtain analytic results which will hold for arbitrary large systems. Recently a statistical ensemble of random graphs with a regular block structure, i.e. the ensemble of equitable graphs, has been introduced and analytic results have been derived in the computationally-hard context of graph partitioning and community detection.

In this paper, we present a general analytic result for a ensemble of equitable core–periphery graphs, yielding a new explicit formula for the spectral density of networks with core–periphery structure.

核心－外围结构是各种复杂系统的新兴属性，它表明系统中存在一组参与者，参与者之间的联系数量较高，与稀疏连接的外围设备的联系数量较少。在给定图结构上相互作用的复杂系统的动力学与图本身的光谱特性严格相关，但是，通常很难获得适用于任意大型系统的分析结果。最近，引入了具有规则块结构的随机图的统计集合，即等价图的集合，并且在图划分和社区检测的计算困难的情况下得出了分析结果。

在本文中，我们给出了一组相等的核心-外围图的一般分析结果，从而为具有核心-外围结构的网络的频谱密度提供了一个新的显式公式。