A novel framework for outlier detection in financial markets: a complex network approach with visibility graphs

Introduction The increasing complexity and non-linearity of financial markets make traditional linear models inadequate for systemic risk assessments. This study aims to develop a new framework for identifying outlier events and critical transitions in financial markets. Methods We propose a framework that combines a complex network approach with visibility graph algorithms. First, a comprehensive financial stress index (FSI) for China is constructed by integrating sub-indices from the bond, stock, money, and foreign exchange markets, along with time-varying cross-market correlations. The FSI and sub-index time series are converted into complex networks via the visibility graph algorithm. A Rayleigh-entropy-based overlapping influence algorithm is introduced to detect critical risk nodes, addressing node interdependencies and network loops overlooked by traditional percolation theories. The framework is validated using daily data from January 2015 to June 2025, with cross-market stress transmission examined through a vector autoregression model. Results The approach effectively identifies major financial stress periods and cross-market stress transmission paths. A stock market shock raises the bond market stress index by 0.08 within five trading days. A reserve requirement ratio cut by the People’s Bank of China reduces the average money market stress index by 0.12 within 30 days. Stress originates and spreads across sub-markets with measurable time lags, and the bond market credit spread is the dominant driver of stochastic fluctuations in the FSI. Discussion The proposed network-based method, paired with model-driven transmission analysis, serves as a robust dynamic tool for monitoring and early warning of financial systemic risk. It provides data-supported insights for both academic researchers and policymakers.