Critical Points Identification and Ranking in the Evolution Process of Financial Complex Networks: Visibility Graph model

Against the backdrop of heightened financial market volatility and complex policy interventions, this paper proposes a novel framework to identify and rank critical nodes in the evolution of financial complex networks. First, we construct a composite Financial Complex Networks Index (FCNI) basing the impulse response results of Structural Vector Autoregression model. Second, we employ the horizontal visibility graph (HVG) method to map the FCNI time series into a complex network, which demonstrates that the FCNI degree distribution follows a power-law, confirming the presence of critical nodes that play a pivotal role in network dynamics. Third, by employing a fuzzy TOPSIS method to synthesize multiple centrality indicators into unified composite scores, we identify critical nodes and empirically confirm a robust correspondence between these high-connectedness time points and major macroeconomic events. Finally, these findings provide a scientific basis for early-stage risk warning, suggesting that regulators should adopt node-centric, differentiated policy strategies to effectively mitigate systemic contagion and enhance the overall resilience of the financial system.