Hierarchies in communities of UK stock market from the perspective of Brexit

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.