This paper constructs an institutional investor network based on the heavy holdings of the same stock in China and conducts a social network analysis to investigate the influence of this network on stock price volatility from the perspectives of network structure (density) and location (centrality). The study demonstrates that institutional investor network density is negatively related to stock price volatility, while network centrality is positively related to it. Mechanism analyses further reveal that network density reduces stock price volatility by mitigating private information arbitrage behavior among institutional investors, whereas network centrality increases stock price volatility by creating private information arbitrage opportunities within the network. Additionally, the paper finds that information asymmetry enhances the positive effect of network centrality on stock price volatility. These findings are generally consistent across subsample analyses for different market states, reactions to good and bad news, and types of equity ownership, as well as in other robustness tests. The practical implications of these findings are significant for market stability regulation.