In this project, we propose new methods for the tail dependency network analysis with high-dimensional financial and economic data, which will remedy some of the shortcomings of the existing approaches. Firstly, we study the dependence between individuals' extreme events at different tail risk levels. Secondly, we analyse the financial quantile network effect with possible misspecified network structure. Lastly, we generalise the applicability of the theory to time series with a general dependency measure.