Nowadays, increase of analyzing stock markets as complex systems lead graph theory to play a key role. For instance, detecting graph communities is an important task in the analysis of stocks, and as planar maximally filtered graphs let us to get important information for the topology of the market. In this study, we first obtain correlation network representation of UK's leading stock market network by using a novel threshold method. Then, we determine vertex clusters by using modularity and analyze clusters in planar maximally filtered graph substructures. Our analyze include a new measure called weighted Gini index for measuring the sparsity. The main goal of this paper is to study the hierarchical evolution of the market communities throughout the Brexit referendum, which is known as the stress period for the stock market. Hence, the overall sample is divided into two sub-periods of pre-referendum, and post-referendum to obtain communities and hierarchical structures. Our results indicate that financial companies are leading elements of the clusters. Moreover, the significant changes within the network topologies are observed for insurance, consumer goods, consumer services, mining, and technology sectors whereas oil and gas and health care sectors have not been affected by Brexit stress.

如今，越来越多地将股票市场作为复杂系统进行分析，这使得图论发挥了关键作用。例如，检测图社区是股票分析中的一项重要任务，作为平面最大过滤图，我们可以获取市场拓扑结构的重要信息。在这项研究中，我们首先使用一种新的阈值方法获得了英国领先股票市场网络的相关网络表示。然后，我们通过使用模块化来确定顶点簇，并分析平面最大滤波图子结构中的簇。我们的分析包括一种称为加权基尼指数的新方法，用于测量稀疏度。本文的主要目标是研究整个英国脱欧公投期间市场社区的等级演变，这被称为股市的压力期。因此，整体样本分为公投前和公投后两个子时期，以获得社区和等级结构。我们的结果表明，金融公司是集群的主要元素。此外，在保险、消费品、消费服务、采矿和技术部门观察到网络拓扑结构发生重大变化，而石油和天然气以及医疗保健部门并未受到英国退欧压力的影响。